The original problem for thermally developing heat transfer in laminar flow through a circular tube, as formulated by Graetz, did not consider the ’slip-flow’ condition. This paper extends the original work of Graetz to include the effect of slip-flow, which occurs in gases at low pressures or in microtubes at ordinary pressures. A special technique was developed to evaluate the eigenvalues for the problem. Eigenvalues were evaluated for Knudsen numbers ranging between 0 and 0.12. Simplified relationships were developed to describe the effect of slip-flow on the convection heat transfer coefficient.