The effect of a temperature dependent variable viscosity fluid flow down an inclined plane with a free surface is investigated.The
fluid film is thin, so that lubrication approximation may be applied. Convective heating effects are included, and the fluid viscosity
decreases exponentially with temperature. In general, the flow equations resulting from the variable viscosity model must be solved
numerically. However, when the viscosity variation is small, then an asymptotic approximation is possible. The full solutions for
the temperature and velocity profiles are derived using the Runge-Kutta numerical method.The flow controlling parameters such
as the nondimensional viscosity variation parameter, the Biot and the Brinkman numbers, are found to have a profound effect on
the resulting flow profiles.