Conjugate heat transfer in a microtube gas flow with constant wall temperature boundary condition is studied numerically, taking into consideration the effects of the shear work, axial conduction rarefaction, pressure work and viscous dissipation. Analytical solutions for the case with non-zero Brinkman number are also obtained. The effect of the tube wall thickness and the wall thermal conductivity on Nusselt number, inner wall heat flux, bulk gas temperature, inner wall temperature and other heat transfer characteristics are analyzed. Comparisons with the standard zero wall thickness case are also presented. The results illustrate the significance of the wall heat conduction on the thermal entrance length and the heat transfer characteristics in the microtube in the thermally developing and the fully developed flow regions, and show the deviation from those with zero wall thickness. The analysis shows that in the thermally fully developed region, the Nusselt number and the heat flux at the inner wall are however, not influenced by the tube wall heat conduction. Heat exchange between the gas and the wall is shown to take place only in the thermal entrance region.