An approximate procedure is developed for determining the heat sink capability of an interline region (junction of vapor, evaporating thin film, and nonevaporating thin film), with consideration of the effect of resistance of the solid to heat transfer. The formulation is based on a simple one-dimensional constant heat flux model. The solution is directed toward a limiting case in which the thermal conductance of the solid is controlling. Since the value of the ideal liquid-vapor interfacial heat transfer coefficient is very large, conductance of the solid is found to dominate the overall heat transfer coefficient in the interline region after a small increase in film thickness.