In this paper, three-dimensional numerical simulations of the transcritical flow and heat transfer of methane are performed in a rectangular channel under asymmetric heating. The accuracy of four different Nusselt number correlations in the calculation of transcritical methane flow and heat transfer is compared, and two improved heat transfer correlations are proposed based on the Bishop correlation with and without adding a velocity profile correction term. The obtained results show that the proposed heat transfer correlations can accurately predict the heat transfer of transcritical methane. It is also shown that by adding a velocity profile correction term, the error between calculated values and those obtained from numerical simulations is reduced from 6.33% to 2.82%. Moreover, it is revealed that under severe heat transfer deterioration conditions, the proposed heat transfer correlations overestimate the convective heat transfer coefficient near the inlet. When the heat transfer is significantly improved, the variation of convective heat transfer coefficient becomes very different from the base case. A large error is noticed between the calculated results of correlation Modified 1 and the results obtained from the numerical simulations, while the correlation Modified 2 with velocity profile correction term still proves satisfactory calculation accuracy.