A comparative study of supercritical heat transfer in a regeneratively cooled rocket engine was conducted using three-dimensional numerical simulations for two channel geometries: rectangular and square. Various constant heat fluxes, flow velocities, and operating pressures were imposed to study their effect on heat transfer, pressure losses, and the conditions under which heat transfer deterioration HTD occurs. The results show that a rectangular channel is more efficient in terms of heat transfer than a square channel, with a more pronounced difference at high heat fluxes and low velocities, these conditions, in fact, favored the occurrence of heat transfer deterioration, particularly in the square channel. Increasing the flow velocities to reduce the wall temperature and prevent thermal deterioration was accompanied by a significant increase in pressure losses, these pressure losses are greater in the rectangular channel, despite its advantages in terms of heat transfer. Operating pressure also plays an important role in heat transfer, increasing the pressure results in a decrease in wall temperature.