With reference to the stationary and laminar forced convection in a circular duct for an incompressible Newtonian fluid having a fully developed velocity profile, previous studies on the existence of an asymptotic thermally developed region are improved. A sufficient condition, much broader than those previously found in the literature for the existence of an asymptotic thermally developed region, is determined. It is proved that this condition is also necessary if one requires that the asymptotic value of the Nusselt number is nonzero. A numerical computation of the temperature field in the thermal entrance region for two different wall heat flux distributions which Fulfil the sufficient condition for the existence of an asymptotic thermally developed region and which yield the same asymptotic value of the Nusselt number is performed.