Capillary surface wetting is a passive phenomenon that depends on free surface energies. As heat transfer rates increase, within limits, more liquid flows onto the surface and evaporates. The differential equations describing mass and heat transfer mechanisms have been solved simultaneously for several capillary groove configurations. Further, by methods outlined in this paper, the effects of solid-liquid-vapor interline heat transfer phenomena can be isolated and evaluated. Not only does this provide a method for predicting surface heat transfer coefficients for surfaces wetted through capillary grooves, it also provides basic information about heat transfer in the vicinity of the meniscus attachment region.