A numerical solution of the thermal entry length problem for circular pipes with constant temperature boundaries and with a prescribed dependence of viscosity on temperature and viscous dissipation of some specified order are presented. The results indicate a significant effect of these factors. The results for both heating and cooling processes are presented and compared with the available analytical results. They are useful in the design of heat exchangers with high Prandtl number fluids as the working media. © 1978 Springer-Verlag.