We prove sharp two sided heat kernel estimates on a connected sum of two copies of R n along a surface of revolution taking into account a bottleneck effect. In the proof, estimates of the hitting probability of a non-compact set play a crucial role. For the heat kernel upper bound, we use isoperimetric inequalities on connected sums. For the heat kernel lower bound, we use a lower bound of the Dirichlet heat kernel in the exterior of a non-compact set.