The effect of viscous dissipation and applied magnetic field is investigated for the case of the fully developed natural convection of a fluid between two heated walls. When electrical and viscous dissipation is negligible, short-circuited Hartmann flow results. The deviation of the velocity and temperature profiles from those existing in Hartmann flow are presented for various Hartmann numbers when dissipation is not neglected. It is shown that increasing the applied magnetic field rapidly decreases the influence of both viscous and joulean dissipation on the velocity and temperature profiles.