This paper deals with an analysis to determine the heat transfer characteristics of the thermal entrance region for an established laminar flow of a heat generating Bingham plastic through a circular tube with wall heat transfer. The conditions of wall heat transfer treated in this paper are both the case of prescribed uniform wall heat flux and that of uniform wall temperature. In this analysis, eigenvalues and eigenfunctions are evaluated by means of a digital computer KDC-1. The heat transfer characteristics approach those of a fully developed region which were calculated in the previous paper by one of the authors. The results for a Newtonian fluid flow which were analyzed as a special case agree very well with those by Nusselt and Siegel et al.