Prediction of heat transfer deterioration in rocket engine coolant channels with supercritical flow is essential while designing high pressure rocket engines. Three-dimensional conjugate heat transfer of cryogenic methane in rectangular engine cooling channels at  supercritical pressures with asymmetric heating imposed on the bottom  channel surface is numerically investigated, focusing  on the effects of  key parameters such as  aspect ratio, heat flux and coolant pressure. Due to the similarity of the coolant channel with that of an actual rocket engine, the results obtained herein are beneficial for the design and optimization of rocket engine cooling systems. Heat flux is varied from 1 MW/m² to 5 MW/m² and the coolant pressure from 6 MPa to 12 MPa. Results indicate that the aspect ratio has significant effect on the conjugate heat transfer owing to heat flux re-distribution in the walls. From the heat transfer point of view, channels with high aspect ratio perform well. Heat transfer deterioration is observed due to the drastic property variation near pseudocritical temperature in the region close to the wall. Increasing the operating pressure would result in improved heat transfer at supercritical pressures, particularly under high wall heat fluxes.