This paper presents numerical results for two-dimensional steady-state natural convection in a square cavity. The upper and lower walls are kept at different constant temperatures, whereas the lateral walls have certain thickness and thermal conductivity and are externally insulated. Under these conditions we deal with a conjugate natural convection problem in which the heat conduction in the lateral walls is coupled with the internal convection. The continuity, momentum and energy equations were solved by using the finite volume method. The results here presented include: (i) the temperature distribution in the lateral walls and in the fluid, (ii) the velocity field, and (iii) the average Nusselt number at the upper and lower walls. It was found that the steady state fluid flow is strongly dependent on the initial temperature condition, when the fluid is initially at rest. The PIV technique allowed us to get some experimental data by measuring the velocity field in a two-dimensional square cavity. A good agreement between numerical and experimental results was found.