Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 a parts per thousand currency sign Ra a parts per thousand currency sign 1000), the internal heating and the local exponent parameters (0 a parts per thousand currency sign gamma a parts per thousand currency sign 5), (1 a parts per thousand currency sign lambda a parts per thousand currency sign 3), the wall to porous thermal conductivity ratio (0.44 a parts per thousand currency sign Kr a parts per thousand currency sign 9.9) and the ratio of wall thickness to its width (0.02 a parts per thousand currency sign D a parts per thousand currency sign 0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.