The combined natural- and forced convection flow of a viscous, electrically conducting liquid between parallel electrically conducting walls, in the presence of a transverse magnetic field is analysed. The walls are taken to be at temperatures linearly varying along their lengths. The resulting non-linear differential equations are solved in terms of even and odd functions depending on the Hartmann number and a modified Rayleigh number, so that solutions for a variety of conditions may be easily computed from their values. The cumulative effect of dissipative and Joule heating are found to be negligible. The Nusselt numbers and viscous drag are found to diminish with increase of the conductivities of the walls.