diff --git a/CHANGELOG.md b/CHANGELOG.md
index c477799b25..8b962a9f0e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,7 @@
 
 ## Features
 
+-   Added tab, edge, and surface cooling ([#965](https://github.com/pybamm-team/PyBaMM/pull/965))
 -   Added functionality to solver to automatically discretise a 0D model ([#947](https://github.com/pybamm-team/PyBaMM/pull/947))
 -   Added sensitivity to `CasadiAlgebraicSolver` ([#940](https://github.com/pybamm-team/PyBaMM/pull/940))
 -   Added `ProcessedSymbolicVariable` class, which can handle symbolic variables (i.e. variables for which the inputs are symbolic) ([#940](https://github.com/pybamm-team/PyBaMM/pull/940))
diff --git a/examples/notebooks/using-model-options_thermal-example.ipynb b/examples/notebooks/using-model-options_thermal-example.ipynb
index 851ae6ef5a..6a089069c7 100644
--- a/examples/notebooks/using-model-options_thermal-example.ipynb
+++ b/examples/notebooks/using-model-options_thermal-example.ipynb
@@ -65,7 +65,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We choose to use the parameters from [1]. We then update the heat transfer coefficient to be 0.1 [W/m^2/K] (see the [Parameter Values notebook](./parameter-values.ipynb) for more details)"
+    "We choose to use the parameters from [1]. We then update the heat transfer coefficients (see the [Parameter Values notebook](./parameter-values.ipynb) for more details)"
    ]
   },
   {
@@ -75,7 +75,17 @@
    "outputs": [],
    "source": [
     "param = pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019)\n",
-    "param.update({\"Heat transfer coefficient [W.m-2.K-1]\": 0.1})"
+    "param.update(\n",
+    "    {\n",
+    "        \"Negative current collector\"\n",
+    "        + \" surface heat transfer coefficient [W.m-2.K-1]\": 5,\n",
+    "        \"Positive current collector\"\n",
+    "        + \" surface heat transfer coefficient [W.m-2.K-1]\": 5,\n",
+    "        \"Negative tab heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "        \"Positive tab heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "        \"Edge heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "    }\n",
+    ")"
    ]
   },
   {
@@ -121,7 +131,7 @@
    "source": [
     "# solve model\n",
     "solver = model.default_solver\n",
-    "t_eval = np.linspace(0, 1, 250)\n",
+    "t_eval = np.linspace(0, 3600, 250)\n",
     "solution = solver.solve(model, t_eval)"
    ]
   },
@@ -140,12 +150,12 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "c3d04dd597c24caf83c370bd01fe6131",
+       "model_id": "115696cc7c7e4297bb6d85a9f8220a82",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=3599.9999999999995, step=35.99999999999999),…"
       ]
      },
      "metadata": {},
@@ -202,9 +212,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
\ No newline at end of file
+}
diff --git a/examples/scripts/thermal_lithium_ion.py b/examples/scripts/thermal_lithium_ion.py
index f9766b4f0d..cd4c1fbdea 100644
--- a/examples/scripts/thermal_lithium_ion.py
+++ b/examples/scripts/thermal_lithium_ion.py
@@ -18,7 +18,20 @@
 
 # load parameter values and process models and geometry
 param = models[0].default_parameter_values
-param.update({"Heat transfer coefficient [W.m-2.K-1]": 1})
+
+# for x-full, cooling is only implemented on the surfaces
+# so set other forms of cooling to zero for comparison.
+param.update(
+    {
+        "Negative current collector"
+        + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+        "Positive current collector"
+        + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+        "Negative tab heat transfer coefficient [W.m-2.K-1]": 0,
+        "Positive tab heat transfer coefficient [W.m-2.K-1]": 0,
+        "Edge heat transfer coefficient [W.m-2.K-1]": 0,
+    }
+)
 
 for model in models:
     param.process_model(model)
diff --git a/pybamm/input/parameters/lead-acid/experiments/1C_discharge_from_full/parameters.csv b/pybamm/input/parameters/lead-acid/experiments/1C_discharge_from_full/parameters.csv
index 154de5565e..18cc3b5eac 100644
--- a/pybamm/input/parameters/lead-acid/experiments/1C_discharge_from_full/parameters.csv
+++ b/pybamm/input/parameters/lead-acid/experiments/1C_discharge_from_full/parameters.csv
@@ -5,8 +5,11 @@ Name [units],Value,Reference,Notes
 Reference temperature [K],294.85,Room temperature,
 Maximum temperature [K],333.15,,
 Ambient temperature [K], 294.85,,
-Heat transfer coefficient [W.m-2.K-1],10,,
-Initial temperature [K],294.85,Room temperature,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 
 ,,,
 # Electrical
@@ -18,3 +21,4 @@ Upper voltage cut-off [V],2.44,(just over) 14.5V across 6-cell battery,
 # Initial conditions
 Initial State of Charge,1,-,
 Initial oxygen concentration [mol.m-3],0,,
+Initial temperature [K],294.85,Room temperature,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_charge_from_empty_Mohtat2020/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_charge_from_empty_Mohtat2020/parameters.csv
index ae32f40bb8..e843bfe334 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_charge_from_empty_Mohtat2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_charge_from_empty_Mohtat2020/parameters.csv
@@ -3,10 +3,14 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],5,Peyman MPM,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],0,,
+Positive tab heat transfer coefficient [W.m-2.K-1],0,,
+Edge heat transfer coefficient [W.m-2.K-1],5,Peyman MPM,
 Ambient temperature [K], 298.15,,
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],2.5,,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
index 7f59fcfd10..d91bb6f89b 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
@@ -3,11 +3,15 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],10,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 Ambient temperature [K], 298.15,,
 
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],2.5,,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ecker2015/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ecker2015/parameters.csv
index 131c087945..0397997a1b 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ecker2015/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ecker2015/parameters.csv
@@ -3,7 +3,11 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],296.15,23C,
-Heat transfer coefficient [W.m-2.K-1],10, The paper does not consider thermal effects so a typical value is chosen,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,Paper does not consider thermal effects
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,Paper does not consider thermal effects
+Negative tab heat transfer coefficient [W.m-2.K-1],10,Paper does not consider thermal effects,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,Paper does not consider thermal effects,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,Paper does not consider thermal effects,
 Ambient temperature [K], 298.15,,
 
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Kim2011/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Kim2011/parameters.csv
index e1e4b77c65..4d475c47e8 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Kim2011/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Kim2011/parameters.csv
@@ -3,7 +3,11 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],25,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],25,,
+Positive tab heat transfer coefficient [W.m-2.K-1],25,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 Ambient temperature [K], 298.15,,
 
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Marquis2019/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Marquis2019/parameters.csv
index bd463472c5..fb80497c1a 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Marquis2019/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Marquis2019/parameters.csv
@@ -4,9 +4,13 @@ Name [units],Value,Reference,Notes
 # Temperature
 Reference temperature [K],298.15,25C,
 Ambient temperature [K], 298.15,,
-Heat transfer coefficient [W.m-2.K-1],10,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],3.105,,
diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py
index 4e4c2673f6..606142a5c4 100644
--- a/pybamm/models/full_battery_models/base_battery_model.py
+++ b/pybamm/models/full_battery_models/base_battery_model.py
@@ -3,6 +3,7 @@
 #
 
 import pybamm
+import warnings
 
 
 class BaseBatteryModel(pybamm.BaseModel):
@@ -239,6 +240,12 @@ def options(self, extra_options):
                 "particle model '{}' not recognised".format(options["particle"])
             )
 
+        if options["thermal"] == "x-lumped" and options["dimensionality"] == 1:
+            warnings.warn(
+                "1+1D Thermal models are only valid if both tabs are"
+                + "placed at the top of the cell."
+            )
+
         self._options = options
 
     def set_standard_output_variables(self):
diff --git a/pybamm/models/submodels/thermal/lumped.py b/pybamm/models/submodels/thermal/lumped.py
index 3b4a63dc9e..78fe5e525c 100644
--- a/pybamm/models/submodels/thermal/lumped.py
+++ b/pybamm/models/submodels/thermal/lumped.py
@@ -53,12 +53,47 @@ def set_rhs(self, variables):
         # the choice of non-dimensionalisation.
         # TODO: allow for arbitrary surface area to volume ratio in order to model
         # different cell geometries (see #718)
-        A = self.param.l_y * self.param.l_z
-        V = self.param.l * self.param.l_y * self.param.l_z
-        cooling_coeff = -2 * self.param.h * A / V / (self.param.delta ** 2)
+        cell_volume = self.param.l * self.param.l_y * self.param.l_z
+
+        yz_cell_surface_area = self.param.l_y * self.param.l_z
+        yz_surface_cooling_coefficient = (
+            -(self.param.h_cn + self.param.h_cp)
+            * yz_cell_surface_area
+            / cell_volume
+            / (self.param.delta ** 2)
+        )
+
+        negative_tab_area = self.param.l_tab_n * self.param.l_cn
+        negative_tab_cooling_coefficient = (
+            -self.param.h_tab_n * negative_tab_area / cell_volume / self.param.delta
+        )
+
+        positive_tab_area = self.param.l_tab_p * self.param.l_cp
+        positive_tab_cooling_coefficient = (
+            -self.param.h_tab_p * positive_tab_area / cell_volume / self.param.delta
+        )
+
+        edge_area = (
+            2 * self.param.l_y * self.param.l
+            + 2 * self.param.l_z * self.param.l
+            - negative_tab_area
+            - positive_tab_area
+        )
+        edge_cooling_coefficient = (
+            -self.param.h_edge * edge_area / cell_volume / self.param.delta
+        )
+
+        total_cooling_coefficient = (
+            yz_surface_cooling_coefficient
+            + negative_tab_cooling_coefficient
+            + positive_tab_cooling_coefficient
+            + edge_cooling_coefficient
+        )
 
         self.rhs = {
-            T_vol_av: (self.param.B * Q_vol_av + cooling_coeff * (T_vol_av - T_amb))
+            T_vol_av: (
+                self.param.B * Q_vol_av + total_cooling_coefficient * (T_vol_av - T_amb)
+            )
             / (self.param.C_th * self.param.rho)
         }
 
diff --git a/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_1D_current_collectors.py b/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_1D_current_collectors.py
index 1fb3a43529..3b47bf1604 100644
--- a/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_1D_current_collectors.py
+++ b/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_1D_current_collectors.py
@@ -60,15 +60,30 @@ def set_rhs(self, variables):
         # Account for surface area to volume ratio of pouch cell in cooling
         # coefficient. Note: the factor 1/delta^2 comes from the choice of
         # non-dimensionalisation
-        A = self.param.l_y * self.param.l_z
-        V = self.param.l * self.param.l_y * self.param.l_z
-        cooling_coeff = -2 * self.param.h * A / V / (self.param.delta ** 2)
+        cell_volume = self.param.l * self.param.l_y * self.param.l_z
+
+        yz_surface_area = self.param.l_y * self.param.l_z
+        yz_surface_cooling_coefficient = (
+            -(self.param.h_cn + self.param.h_cp)
+            * yz_surface_area
+            / cell_volume
+            / (self.param.delta ** 2)
+        )
+
+        side_edge_area = 2 * self.param.l_z * self.param.l
+        side_edge_cooling_coefficient = (
+            -self.param.h_edge * side_edge_area / cell_volume / self.param.delta
+        )
+
+        total_cooling_coefficient = (
+            yz_surface_cooling_coefficient + side_edge_cooling_coefficient
+        )
 
         self.rhs = {
             T_av: (
                 pybamm.laplacian(T_av)
                 + self.param.B * Q_av
-                + cooling_coeff * (T_av - T_amb)
+                + total_cooling_coefficient * (T_av - T_amb)
             )
             / (self.param.C_th * self.param.rho)
         }
@@ -76,24 +91,51 @@ def set_rhs(self, variables):
     def set_boundary_conditions(self, variables):
         T_amb = variables["Ambient temperature"]
         T_av = variables["X-averaged cell temperature"]
-        T_av_left = pybamm.boundary_value(T_av, "negative tab")
-        T_av_right = pybamm.boundary_value(T_av, "positive tab")
+        T_av_top = pybamm.boundary_value(T_av, "right")
+        T_av_bottom = pybamm.boundary_value(T_av, "left")
+
+        # Tab cooling only implemented for both tabs at the top.
+        negative_tab_area = self.param.l_tab_n * self.param.l_cn
+        positive_tab_area = self.param.l_tab_p * self.param.l_cp
+        total_top_area = self.param.l * self.param.l_y
+        non_tab_top_area = total_top_area - negative_tab_area - positive_tab_area
+
+        negative_tab_cooling_coefficient = (
+            self.param.h_tab_n / self.param.delta * negative_tab_area / total_top_area
+        )
+        positive_tab_cooling_coefficient = (
+            self.param.h_tab_p / self.param.delta * positive_tab_area / total_top_area
+        )
+
+        top_edge_cooling_coefficient = (
+            self.param.h_edge / self.param.delta * non_tab_top_area / total_top_area
+        )
+
+        bottom_edge_cooling_coefficient = (
+            self.param.h_edge / self.param.delta * total_top_area / total_top_area
+        )
+
+        total_top_cooling_coefficient = (
+            negative_tab_cooling_coefficient
+            + positive_tab_cooling_coefficient
+            + top_edge_cooling_coefficient
+        )
+
+        total_bottom_cooling_coefficient = bottom_edge_cooling_coefficient
 
-        # Three boundary conditions here to handle the cases of both tabs at
-        # the same side (top or bottom), or one either side. For both tabs on the
-        # same side, T_av_left and T_av_right are equal, and the boundary condition
-        # "no tab" is used on the other side.
+        # just use left and right for clarity
+        # left = bottom of cell (z=0)
+        # right = top of cell (z=L_z)
         self.boundary_conditions = {
             T_av: {
-                "negative tab": (
-                    self.param.h * (T_av_left - T_amb) / self.param.delta,
+                "left": (
+                    total_bottom_cooling_coefficient * (T_av_bottom - T_amb),
                     "Neumann",
                 ),
-                "positive tab": (
-                    -self.param.h * (T_av_right - T_amb) / self.param.delta,
+                "right": (
+                    -total_top_cooling_coefficient * (T_av_top - T_amb),
                     "Neumann",
                 ),
-                "no tab": (pybamm.Scalar(0), "Neumann"),
             }
         }
 
diff --git a/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_2D_current_collectors.py b/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_2D_current_collectors.py
index 8901318dc9..36aa2e5a51 100644
--- a/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_2D_current_collectors.py
+++ b/pybamm/models/submodels/thermal/pouch_cell/pouch_cell_2D_current_collectors.py
@@ -60,34 +60,61 @@ def set_rhs(self, variables):
         # Account for surface area to volume ratio of pouch cell in cooling
         # coefficient. Note: the factor 1/delta^2 comes from the choice of
         # non-dimensionalisation
-        A = self.param.l_y * self.param.l_z
-        V = self.param.l * self.param.l_y * self.param.l_z
-        cooling_coeff = -2 * self.param.h * A / V / (self.param.delta ** 2)
+        yz_surface_area = self.param.l_y * self.param.l_z
+        cell_volume = self.param.l * self.param.l_y * self.param.l_z
+        yz_surface_cooling_coefficient = (
+            -(self.param.h_cn + self.param.h_cp)
+            * yz_surface_area
+            / cell_volume
+            / (self.param.delta ** 2)
+        )
+
+        edge_cooling_coefficient = self.param.h_edge / self.param.delta
 
-        # Add boundary source term which accounts for surface cooling around
-        # the edge of the domain in the weak formulation.
-        # TODO: update to allow different cooling conditions at the tabs
+        # Governing equations contain:
+        #   - source term for y-z surface cooling
+        #   - boundary source term of edge cooling
+        # Boundary conditions contain:
+        #   - Neumann condition for tab cooling
         self.rhs = {
             T_av: (
                 pybamm.laplacian(T_av)
                 + self.param.B * pybamm.source(Q_av, T_av)
-                + cooling_coeff * pybamm.source(T_av - T_amb, T_av)
-                - (self.param.h / self.param.delta)
+                + yz_surface_cooling_coefficient * pybamm.source(T_av - T_amb, T_av)
+                - edge_cooling_coefficient
                 * pybamm.source(T_av - T_amb, T_av, boundary=True)
             )
             / (self.param.C_th * self.param.rho)
         }
 
+        # TODO: Make h_edge a function of position to have bottom/top/side cooled cells.
+
     def set_boundary_conditions(self, variables):
         T_av = variables["X-averaged cell temperature"]
-        # Dummy no flux boundary conditions since cooling at the the tabs is
-        # accounted for in the boundary source term in the weak form of the
-        # governing equation
-        # TODO: update to allow different cooling conditions at the tabs
+        T_amb = variables["Ambient temperature"]
+
+        # Subtract the edge cooling from the tab portion so as to not double count
+        # Note: tab cooling is also only applied on the current collector hence
+        # the (l_cn / l) and (l_cp / l) prefactors.
+        # We also still have edge cooling on the region: x in (0, 1)
+        h_tab_n_corrected = (
+            (self.param.l_cn / self.param.l)
+            * (self.param.h_tab_n - self.param.h_edge)
+            / self.param.delta
+        )
+        h_tab_p_corrected = (
+            (self.param.l_cp / self.param.l)
+            * (self.param.h_tab_p - self.param.h_edge)
+            / self.param.delta
+        )
+
+        T_av_n = pybamm.BoundaryValue(T_av, "negative tab")
+        T_av_p = pybamm.BoundaryValue(T_av, "positive tab")
+
         self.boundary_conditions = {
             T_av: {
-                "negative tab": (pybamm.Scalar(0), "Neumann"),
-                "positive tab": (pybamm.Scalar(0), "Neumann"),
+                "negative tab": (-h_tab_n_corrected * (T_av_n - T_amb), "Neumann"),
+                "positive tab": (-h_tab_p_corrected * (T_av_p - T_amb), "Neumann"),
             }
         }
 
diff --git a/pybamm/models/submodels/thermal/x_full.py b/pybamm/models/submodels/thermal/x_full.py
index 22ebb8a745..41f8d75d94 100644
--- a/pybamm/models/submodels/thermal/x_full.py
+++ b/pybamm/models/submodels/thermal/x_full.py
@@ -51,6 +51,7 @@ def set_rhs(self, variables):
         # Fourier's law for heat flux
         q = -self.param.lambda_k * pybamm.grad(T)
 
+        # N.B only y-z surface cooling is implemented for this model
         self.rhs = {
             T: (-pybamm.div(q) / self.param.delta ** 2 + self.param.B * Q)
             / (self.param.C_th * self.param.rho_k)
@@ -62,14 +63,16 @@ def set_boundary_conditions(self, variables):
         T_p_right = pybamm.boundary_value(T, "right")
         T_amb = variables["Ambient temperature"]
 
+        # N.B only y-z surface cooling is implemented for this thermal model.
+        # Tab and edge cooling is not accounted for.
         self.boundary_conditions = {
             T: {
                 "left": (
-                    self.param.h * (T_n_left - T_amb) / self.param.lambda_n,
+                    self.param.h_cn * (T_n_left - T_amb) / self.param.lambda_n,
                     "Neumann",
                 ),
                 "right": (
-                    -self.param.h * (T_p_right - T_amb) / self.param.lambda_p,
+                    -self.param.h_cp * (T_p_right - T_amb) / self.param.lambda_p,
                     "Neumann",
                 ),
             }
diff --git a/pybamm/parameters/standard_parameters_lead_acid.py b/pybamm/parameters/standard_parameters_lead_acid.py
index 6cb4516426..fce599c2b1 100644
--- a/pybamm/parameters/standard_parameters_lead_acid.py
+++ b/pybamm/parameters/standard_parameters_lead_acid.py
@@ -458,7 +458,13 @@ def U_p_dimensional(c_e, T):
 lambda_k = pybamm.thermal_parameters.lambda_k
 
 Theta = pybamm.thermal_parameters.Theta
-h = pybamm.thermal_parameters.h
+
+h_edge = pybamm.thermal_parameters.h_edge
+h_tab_n = pybamm.thermal_parameters.h_tab_n
+h_tab_p = pybamm.thermal_parameters.h_tab_p
+h_cn = pybamm.thermal_parameters.h_cn
+h_cp = pybamm.thermal_parameters.h_cp
+
 B = (
     i_typ
     * R
diff --git a/pybamm/parameters/standard_parameters_lithium_ion.py b/pybamm/parameters/standard_parameters_lithium_ion.py
index 0571fa9cb6..499d73569f 100644
--- a/pybamm/parameters/standard_parameters_lithium_ion.py
+++ b/pybamm/parameters/standard_parameters_lithium_ion.py
@@ -381,7 +381,13 @@ def chi(c_e):
 lambda_k = pybamm.thermal_parameters.lambda_k
 
 Theta = pybamm.thermal_parameters.Theta
-h = pybamm.thermal_parameters.h
+
+h_edge = pybamm.thermal_parameters.h_edge
+h_tab_n = pybamm.thermal_parameters.h_tab_n
+h_tab_p = pybamm.thermal_parameters.h_tab_p
+h_cn = pybamm.thermal_parameters.h_cn
+h_cp = pybamm.thermal_parameters.h_cp
+
 B = (
     i_typ
     * R
diff --git a/pybamm/parameters/thermal_parameters.py b/pybamm/parameters/thermal_parameters.py
index 76ce5e850d..2c3a45ba3c 100644
--- a/pybamm/parameters/thermal_parameters.py
+++ b/pybamm/parameters/thermal_parameters.py
@@ -55,13 +55,18 @@
 ) / pybamm.geometric_parameters.L
 
 # Cooling coefficient
-h_dim = pybamm.Parameter("Heat transfer coefficient [W.m-2.K-1]")
+h_cn_dim = pybamm.Parameter(
+    "Negative current collector surface heat transfer coefficient [W.m-2.K-1]"
+)
+h_cp_dim = pybamm.Parameter(
+    "Positive current collector surface heat transfer coefficient [W.m-2.K-1]"
+)
+h_tab_n_dim = pybamm.Parameter("Negative tab heat transfer coefficient [W.m-2.K-1]")
+h_tab_p_dim = pybamm.Parameter("Positive tab heat transfer coefficient [W.m-2.K-1]")
+h_edge_dim = pybamm.Parameter("Edge heat transfer coefficient [W.m-2.K-1]")
 
 # Typical temperature rise
-Phi_dim = pybamm.Scalar(1)  # typical scale for voltage drop across cell (order 1V)
-Delta_T = (
-    pybamm.electrical_parameters.i_typ * Phi_dim / h_dim
-)  # computed from balance of typical cross-cell Ohmic heating with surface heat loss
+Delta_T = pybamm.Scalar(1)
 
 # Initial temperature
 T_init_dim = pybamm.Parameter("Initial temperature [K]")
@@ -99,7 +104,13 @@
 
 
 Theta = Delta_T / T_ref
-h = h_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+
+h_edge = h_edge_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+h_tab_n = h_tab_n_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+h_tab_p = h_tab_p_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+h_cn = h_cn_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+h_cp = h_cp_dim * pybamm.geometric_parameters.L_x / lambda_eff_dim
+
 
 T_init = (T_init_dim - T_ref) / Delta_T
 
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
index 63a076abf7..30eecc79ab 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
@@ -64,6 +64,20 @@ def test_compare_outputs_thermal(self):
         for models in model_combos:
             # load parameter values (same for all models)
             param = models[0].default_parameter_values
+
+            # for x-full, cooling is only implemented on the surfaces
+            # so set other forms of cooling to zero for comparison.
+            param.update(
+                {
+                    "Negative current collector"
+                    + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+                    "Positive current collector"
+                    + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+                    "Negative tab heat transfer coefficient [W.m-2.K-1]": 0,
+                    "Positive tab heat transfer coefficient [W.m-2.K-1]": 0,
+                    "Edge heat transfer coefficient [W.m-2.K-1]": 0,
+                }
+            )
             for model in models:
                 param.process_model(model)
 
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py
new file mode 100644
index 0000000000..22d9ce6d6b
--- /dev/null
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py
@@ -0,0 +1,105 @@
+#
+# Tests for the thermal lithium-ion models produce consistent
+# thermal response
+#
+import pybamm
+import numpy as np
+import unittest
+
+
+class TestThermal(unittest.TestCase):
+    def test_consistent_cooling(self):
+        # use spme for comparison instead of spm as
+        # much larger realistic temperature rises
+        # so that errors can be more easily observed
+        C_rate = 5
+        options = {
+            "thermal": "x-lumped",
+        }
+        spme_1D = pybamm.lithium_ion.SPMe(options=options)
+
+        options = {
+            "thermal": "x-lumped",
+            "current collector": "potential pair",
+            "dimensionality": 1,
+        }
+        spme_1p1D = pybamm.lithium_ion.SPMe(options=options)
+
+        options = {
+            "thermal": "x-lumped",
+            "current collector": "potential pair",
+            "dimensionality": 2,
+        }
+        spme_2p1D = pybamm.lithium_ion.SPMe(options=options)
+
+        models = {"SPMe 1D": spme_1D, "SPMe 1+1D": spme_1p1D, "SPMe 2+1D": spme_2p1D}
+        solutions = {}
+
+        for model_name, model in models.items():
+            var = pybamm.standard_spatial_vars
+            var_pts = {
+                var.x_n: 3,
+                var.x_s: 3,
+                var.x_p: 3,
+                var.r_n: 3,
+                var.r_p: 3,
+                var.y: 5,
+                var.z: 5,
+            }
+            chemistry = pybamm.parameter_sets.NCA_Kim2011
+            parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+
+            # high thermal and electrical conductivity in current collectors
+            parameter_values.update(
+                {
+                    "Negative current collector"
+                    + " surface heat transfer coefficient [W.m-2.K-1]": 10,
+                    "Positive current collector"
+                    + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+                    "Negative tab heat transfer coefficient [W.m-2.K-1]": 250,
+                    "Positive tab heat transfer coefficient [W.m-2.K-1]": 250,
+                    "Edge heat transfer coefficient [W.m-2.K-1]": 100,
+                    "Negative current collector"
+                    + " thermal conductivity [W.m-1.K-1]": 267.467 * 100000,
+                    "Positive current collector"
+                    + " thermal conductivity [W.m-1.K-1]": 158.079 * 100000,
+                    "Negative current collector conductivity [S.m-1]": 1e10,
+                    "Positive current collector conductivity [S.m-1]": 1e10,
+                }
+            )
+
+            solver = pybamm.CasadiSolver(mode="fast")
+            sim = pybamm.Simulation(
+                model,
+                var_pts=var_pts,
+                solver=solver,
+                parameter_values=parameter_values,
+                C_rate=C_rate,
+            )
+            t_eval = np.linspace(0, 3500 / 6, 100)
+            sim.solve(t_eval=t_eval)
+
+            solutions[model_name] = sim.solution[
+                "Volume-averaged cell temperature [K]"
+            ].entries
+
+        # check volume-averaged cell temperature is within
+        # 1e-5 relative error
+
+        def err(a, b):
+            return np.max(np.abs(a - b)) / np.max(np.abs(a))
+
+        self.assertGreater(1e-5, err(solutions["SPMe 1D"], solutions["SPMe 1+1D"]))
+        self.assertGreater(1e-5, err(solutions["SPMe 1D"], solutions["SPMe 2+1D"]))
+        self.assertGreater(1e-5, err(solutions["SPMe 1+1D"], solutions["SPMe 2+1D"]))
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    sys.setrecursionlimit(10000)
+
+    if "-v" in sys.argv:
+        debug = True
+    unittest.main()
diff --git a/tests/unit/test_parameters/test_dimensionless_parameter_values_lithium_ion.py b/tests/unit/test_parameters/test_dimensionless_parameter_values_lithium_ion.py
index 7c7dd3000c..cfd5f2869a 100644
--- a/tests/unit/test_parameters/test_dimensionless_parameter_values_lithium_ion.py
+++ b/tests/unit/test_parameters/test_dimensionless_parameter_values_lithium_ion.py
@@ -172,8 +172,6 @@ def test_thermal_parameters(self):
 
         np.testing.assert_almost_equal(values.evaluate(param.Theta / c_rate), 0.008, 2)
 
-        np.testing.assert_almost_equal(values.evaluate(param.h), 3.7881 * 10 ** (-5), 7)
-
         # np.testing.assert_almost_equal(
         #     values.evaluate(param.B / c_rate), 36.216, 2
         # )