An analytical solution for the thermal entry problem for flow in a gap under conditions of fully developed slip flow including axial conduction and temperature jump with an isothermal boundary condition has been acquired by employing a modified generalized integral transform technique. The solutions include effects of rarefaction through the Knudsen number Kn, the fluid/wall interaction through the accommodation coefficients, and axial conduction through the Peclet number. The Nusselt number Nu is shown to increase, decrease, or remain unchanged when compared to the non-slip case depending on the values of the two key nondimensional parameters. When the temperature jump condition is ignored, Nu always increases with increasing Kn. However, for large temperature jump, Nu is reduced significantly with increasing Kn. The Nu decrease can be as much as 90% when compared to the non-slip case. In addition, it is found that the inclusion of axial conduction always increases Nu. A temperature jump transition point has been identified that separates the region of heat transfer enhancement from that of heat transfer reduction.