The formulism of a two-equation model for heat conduction in porous media, developed in a previous paper, is applied to the case of steady state one-dimensional heat transfer in a porous medium that is made up of geometrically similar units of similar size and of ordered spatial distribution. For this case study, the model-predicted locally volume-averaged temperature distributions for the solid and the fluid phase are compared to a numerical solution at a microscopic level, showing excellent agreement.