The heat transfer characteristics of supersonic to hypersonic gas flow in microchannels are numerically studied by solving a two-dimensional Navier-Stokes (NS) system of equations utilizing Maxwell's velocity slip with thermal creep, and a corresponding temperature jump relationship derived by von Smoluchowski. An explicit Finite Volume (FV) solver has been developed using modified advection upwind splitting methods (AUSM+) to simulate the high speed microscale gas flow. The influence of the inlet Mach number on overall hydrodynamics and heat transfer is also studied. The supersonic test case has been compared with the Direct Solution Monte Carlo (DSMC) and Finite Element (FE) results available in the literature. The study of high speed flow through microchannels demonstrates an increase in temperature due to the wall friction and that fluid flow decelerates throughout the microchannels. The wall temperature jump and the centerline temperature are higher for larger inlet Mach numbers.