diff --git a/cpp/src/arrow/acero/query_context.cc b/cpp/src/arrow/acero/query_context.cc
index 9f838508fcd05..a27397d12079d 100644
--- a/cpp/src/arrow/acero/query_context.cc
+++ b/cpp/src/arrow/acero/query_context.cc
@@ -53,7 +53,7 @@ size_t QueryContext::max_concurrency() const { return thread_indexer_.Capacity()
 Result<util::TempVectorStack*> QueryContext::GetTempStack(size_t thread_index) {
   if (!tld_[thread_index].is_init) {
     RETURN_NOT_OK(tld_[thread_index].stack.Init(
-        memory_pool(), 8 * util::MiniBatch::kMiniBatchLength * sizeof(uint64_t)));
+        memory_pool(), 32 * util::MiniBatch::kMiniBatchLength * sizeof(uint64_t)));
     tld_[thread_index].is_init = true;
   }
   return &tld_[thread_index].stack;
diff --git a/cpp/src/arrow/compute/util.cc b/cpp/src/arrow/compute/util.cc
index c55143af0cd59..2058ba9f30757 100644
--- a/cpp/src/arrow/compute/util.cc
+++ b/cpp/src/arrow/compute/util.cc
@@ -32,17 +32,18 @@ using internal::CpuInfo;
 namespace util {
 
 void TempVectorStack::alloc(uint32_t num_bytes, uint8_t** data, int* id) {
-  int64_t old_top = top_;
-  top_ += PaddedAllocationSize(num_bytes) + 2 * sizeof(uint64_t);
-  // Stack overflow check
-  ARROW_DCHECK(top_ <= buffer_size_);
-  *data = buffer_->mutable_data() + old_top + sizeof(uint64_t);
+  int64_t new_top = top_ + PaddedAllocationSize(num_bytes) + 2 * sizeof(uint64_t);
+  // Stack overflow check (see GH-39582).
+  // XXX cannot return a regular Status because most consumers do not either.
+  ARROW_CHECK_LE(new_top, buffer_size_) << "TempVectorStack::alloc overflow";
+  *data = buffer_->mutable_data() + top_ + sizeof(uint64_t);
   // We set 8 bytes before the beginning of the allocated range and
   // 8 bytes after the end to check for stack overflow (which would
   // result in those known bytes being corrupted).
-  reinterpret_cast<uint64_t*>(buffer_->mutable_data() + old_top)[0] = kGuard1;
-  reinterpret_cast<uint64_t*>(buffer_->mutable_data() + top_)[-1] = kGuard2;
+  reinterpret_cast<uint64_t*>(buffer_->mutable_data() + top_)[0] = kGuard1;
+  reinterpret_cast<uint64_t*>(buffer_->mutable_data() + new_top)[-1] = kGuard2;
   *id = num_vectors_++;
+  top_ = new_top;
 }
 
 void TempVectorStack::release(int id, uint32_t num_bytes) {