This paper reports the main results of a series of numerical experiments documenting the phenomenon of convective instability in a horizontal heat-generating porous bed underlying a fluid layer. The problem of interest was modeled with the help of a general flow model for the porous bed. This model accounts for the effects of flow inertia and macroscopic shear in the porous substrate. Both these phenomena are neglected in the more popular Darcy flow model for porous media. The numerical experiments focus primarily on the parametric domain in which the flow in the system is well established, that is, the value of the Rayleigh number is larger than critical. The dependence of the maximum temperature inside the heat-generating porous matrix on the representative dimensionless groups of the problem is predicted. The effect of these groups on the flow field (number, intensity, and shape of convection rolls) and on the temperature field is determined and illustrated for a number of characteristic cases.