Thermal development of forced convection in a circular tube filled with a saturated porous medium, subjected to the constant wall heat flux with a step change including the effect of viscous dissipation and the longitudinal heat conduction, has been studied numerically. Numerical computations for various values of the governing independent parameters, the Peclet number, Pe, the Darcy number, Da, the Brinkman number, Br, and the thermal conductivity ratio, Gamma, were performed to disclose the influence of these parameters on the thermal behavior of flow through the corresponding porous circular tube. Results show that the presence of the viscous dissipation significantly elevates the level of the wall temperature, especially in the downstream region where the wall heat flux is uniformly applied. The local Nusselt number exhibits a monotonically increasing characteristic with the increase in the value of Gamma. Results also show that the effect of the thermal conductivity ratio, Gamma, alters the rate of the wall temperature evolution along the flow direction as well as the transversal profile of the temperature. This implies that the heat transfer is strongly controlled by conduction, and this is significant when the value of the Peclet number, Pe, is small.