In this paper, we use Bejan's Constructal theory to optimize the geometry of a H-shaped cavity that intrudes into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. Internal heat generation is distributed uniformly throughout the solid wall. The cavity surface is isothermal, while the solid wall has adiabatic conditions on the outer surface. The total volume and the volume of the H-shaped cavity are fixed, while the geometry of the H-shaped cavity is free to vary. Numerical results show that the optimal H-shaped configuration performs better than an optimal T-shaped cavity. The performance of the optimal H-shaped cavity is also superior to the performance of optimal rectangular and C-shaped cavities, which may be regarded as "elemental" configurations. Each of the optimized cavities, C-shaped, T-shaped and H-shaped, performs better when it penetrates the solid completely: this means that the geometrical complexity must evolve in order for the global flow system performance to improve. (c) 2006 Elsevier Ltd. All rights reserved.