This investigation addresses the thermogeometric performance of a two-square cavity system contrasted against a two-isosceles triangular cavity system, with an exactly equal heating segment and comparable cooling segment. When one square cavity is cut diagonally in half, it results in a pair of isosceles triangular cavities. The isosceles triangular cavity on the left is heated from the left vertical wall, the top wall is insulated, and the inclined wall is cold; the so-called HIC triangular cavity. The isosceles triangular cavity on the right is heated from the right vertical wall, the bottom wall is insulated, and the inclined wall is cold; the so-called HCI triangular cavity. It may be speculated that the two-isosceles triangular cavity system may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method, accounting for temperature-dependent thermophysical properties of air, is employed to perform the computational analysis. Representative height-based Rayleigh numbers assume values up to to avoid oscillations that occur at a Rayleigh number between and . Numerical results are reported for the velocity field, the temperature field, and the local and the mean convective coefficient along the heated vertical wall. Under a dominant conduction condition for , the heat flux across the derived two-isosceles triangular system is 334% higher than its counterpart across the original two-square system. In contrast, for a dominant convection condition for , this margin diminishes to 20%, but still constitutes a significant improvement. For the design of two-triangular cavity systems, a correlation equation has been constructed yielding a maximum error of 2% at .