The present study deals with computational investigation of natural convection in a porous chamber having a copper finned heat sink and a thermally producing element of finite thickness and heat conductivity. The enclosure is cooled from the external vertical and upper horizontal walls, whilst the remaining borders are considered to be thermally insulated. Newtonian and heat-conducting liquid with temperature-dependent viscosity is assumed as a working medium. Governing equations are written in non-dimensional variables << stream function-vorticity-temperature >> and they are worked out by the finite difference technique. The temperature distribution, streamlines and the dependences of the integral characteristics on the governing characteristics, such as the Darcy and Ostrogradsky numbers and geometric characteristics of the radiator have been illustrated. Presented results can be used for the development of passive cooling systems.