A theoretical analysis is presented for the problem of hydrodynamically developed, thermally developing, steady, laminar forced convective heat transfer of a Newtonian fluid in the entrance region of a microtube. The viscous dissipation effect, the velocity slip, and the temperature jump at the wall are taken into consideration. Two different thermal boundary conditions are considered. the constant heat flux (H1-type) and the constant wall temperature (T-type). Either wall heating (the fluid is heated) or wall cooling (the fluid is cooled) is considered. The downstream variation and the asymptotic value of the Nusselt number are determined as a function of the Brinkman number and the Knudsen number. For softie limiting cases, the results are compared with those existing in the literature and an excellent agreement is observed.