A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.