The problem of a thermally developing forced convective flow in a packed channel heated asymmetrically is analyzed in this paper. The flow in the packed channel is assumed to be hydrodynamically fully developed and is governed by the Brinkman–Darcy–Ergun equation with variable porosity taken into consideration. A closed-form solution based on the method of matched asymptotic expansions is obtained for the axial velocity distribution, and the wall effect on pressure drop is illustrated. The energy equation for the thermally developing flow, with transverse thermal dispersion and variable stagnant thermal conductivity taken into consideration, was solved numerically. To match the predicted temperature distributions with existing experimental data, it is found that a wall function must be introduced to model the transverse thermal dispersion process in order to account for the wall effect on the lateral mixing of fluid. The variations of the local Nusselt number along the streamwise direction in terms of the appropriate parameters are illustrated. The thermal entrance length effect on forced convection in a packed channel is discussed.