The effects of variable viscosity on the surface wave mode of instability of a liquid film flowing down heated or cooled inclined surfaces are examined. Stability boundaries are presented using two models of viscosity variation with temperature. Both models yield qualitatively similar results. It is shown that heating destabilizes the flow, while cooling stabilizes it. For the case of heating the critical wavenumber &agr;cis always zero, while for the case of cooling &agr;ccan be nonzero. By variation of the governing nondimensional parameters, a reasonably complete picture is given when instability occurs first at finite wavelengths.