Two-dimensional flow over a horizontal plate in a saturated porous medium mounted near an impervious adiabatic horizontal surface and subjected to a horizontal forced flow has been numerically investigated. The plate is heated to a uniform temperature that is higher than the temperature of the flowing fluid. The conditions considered are such that the buoyancy forces have an effect on the flow and, therefore, on the heat transfer rate from the plate. The full governing equations, written in dimensionless form, have been solved for a range of values of the governing parameters using the finite element method. The heat transfer rate from the plate is influenced both by the dimensionless depth of the plate below the surface and the importance of the buoyancy forces, the latter having been characterized by a parameter which is equal to the ratio of the Darcy–Rayleigh number to Peclet number. The conditions under which these parameters have a negligible effect on the heat transfer rate are discussed.