Convective heat transfer of a thermally developing rarefied gas flow in a microtube with boundary shear work, viscous dissipation, and axial conduction is analyzed numerically for both constant wall temperature (CWT) and constant wall heat flux (CHF) boundary conditions. Analytical solutions for the fully developed flow conditions including the boundary shear work are also derived. The proper thermal boundary condition considering the sliding friction at the wall for the CHF case is implemented. The sliding friction is also included in the calculation of the wall heat flux for the CWT case. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance—and the fully developed—regions for both gas cooling and heating. Results are presented in both graphical and tabular forms for a range of problem parameters. The results show that the effect of shear work on heat transfer is considerable and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microtube slip flow leads to over- or underestimating the Nusselt number considerably. In particular, for the CWT case with fully developed conditions, the contribution of the shear work to heat transfer can be around 45% in the vicinity of the upper limit of the slip flow regime, regardless of how small the nonzero Brinkman number can be.