The steady-state temperature distribution in stratified two-phase, laminar viscous flow down an inclined solid plane is analyzed. With the plane and atmosphere kept at constant uniform temperatures, the temperature distribution is evaluated for various heat-transfer coefficients at the exposed surface. Graetz’s general approach is adopted here so that this solution holds for arbitrary given temperatures at a transverse section upstream. This method is modified here so as to account for the discontinuities of the physical properties at the interface. This analysis thus yields a detailed account of the heat-transfer mechanism which takes place at the interface.