In this paper, coupled flow and heat transfer by combined convection in a laminar, incompressible, electrically conducting fluid-filled two-dimensional cavity with a thermally isolated body has been analyzed. The developed mathematical model is governed by the conservation of mass, momentum and energy equations and the problem is solved numerically. The effects of two physical parameters namely the Hartmann number Ha and the Reynolds number Re on the flow and heat transfer are discussed and exposed though graphs and tables. The phenomenon inside the cavity for the mentioned parameters is studied through streamline and isotherm patterns. Moreover average Nusselt number which is the representative of heat transfer rate at hot wall is calculated. It is observed that the rate of heat transfer at the bottom heated surface increases with a decrease in Ha, where as it shows reverse effect in case of the Re.