In this paper. the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order slip model is used for the slip-flow and temperature jump boundary conditions for the implementation of the rarefaction effect. Closed form solutions for the temperature field and the fully-developed Nusselt number is derived as a function of Knudsen number, Brinkman number and Peclet number.