The present paper is concerned with the study of flow and heat transfer characteristics in the steady state free convective flow of Al2O3-waternanofluids in a square enclosure in the presence of magnetic field. Attention is given to the temperature variation of the electrical conductivity and its effect on the electromagnetic force induced by the motion of the nanofluid. A new experimental correlation recently presented in the literature was used for this aim. In all the earlier studies in this area the electrical conductivity variation of nanofluid with temperature was neglected. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature and this variation is modeled using the available experimental correlations. The governing differential equations are solved numerically using finite element method. The features of fluid flow and heat transfer characteristics are analyzed for various strengths of the magnetic field and different nanoparticle volume fractions. The results show that when the inclusion of the variation of the electrical conductivity with temperature in the numerical model noticeably affects the natural convection heat transfer in the studied rectangular cavity. The variations of Nusselt number for natural convection of Al2O3-water nanofluid with nanoparticle volume fractions are presented at various Rayleigh and Hartmann numbers.