Two 2D models of non-stationary and non-isothermal transfer of a strong binary electrolyte in a rectangular electrodialysis desalination cell formed by anion- and cation-exchange membranes are developed. Both gravitational and forced convection occurring in underlimiting current mode are taken into account. A boundary problem for the system of equations including Navier-Stokes, Nemst-Planck, Fourier and material balance equations is numerically solved. Results obtained with both models are analyzed and compared. It is shown that the direction of the electric current in the channel is close to perpendicular to the membrane surfaces.