A linear analysis of coupled surface tension and gravity driven instabilities in fluids with variable thermophysical properties is proposed. The fluid layer is initially at rest, of infinite horizontal extent, limited by two flat boundaries and subject to a vertical temperature gradient. Viscosity is supposed to vary exponentially with respect to the temperature, while linear laws are assumed for the heat capacity and thermal conductivity. The relative departure from the Boussinesq model, where fluid properties are constant, is derived by selecting reference properties at the bottom temperature. A physical interpretation of non-Boussinesq effects on the critical threshold is proposed. Computations for glycerol and liquid potassium show that the temperature dependence of the thermophysical properties may have a significant influence on the onset of convection.