Wall-flow monolithic (WFM) catalytic reactors occupy an ever increasing important position in environmental and industrial catalysis as well as in energy applications. Their performance is very frequently determined by transport (momentum, energy, and mass) limitations, driven by the market needs for lower pressure drop, efficient heat exploitation, and miniaturization. In the present problem we address the problem of deriving the appropriate single channel equations that describe heat transfer in a wall-flow monolithic (WFM) reactor with porous channels of square-cross section. The first step of the study involves setting up a self-similar hydrodynamic problem for the two-dimensional flow field in the channel cross section. This flow field depends only on the so-called wall Reynolds number. It is shown that the self-similarity fails for large values of wall Reynolds number. The second step involves setting up the Graetz problem for the flow velocity profile found in the first step and solving for the asymptotic Nusselt number. This Nusselt number depends on the Prandtl number in addition to the wall Reynolds dependence through the flow-field. Correlations for the Nusselt number as a function of wall Reynolds and Prandtl numbers are given to facilitate the inclusion of these effects into standard practice.