Absorption of solar radiation within the thermal molecular sublayer of the ocean can modify the temperature difference across the cool skin as well as the air-sea gas transfer. Our model of renewal type is based on the assumption that the thermal and diffusive molecular sublayers below the ocean surface undergo cyclic growth and destruction, the heat and gas transfer between the successive burst events are performed by molecular diffusion. The model has been upgraded to include heating due to solar radiation. The renewal time is parameterized as a function of the surface Richardson number and the Keulegan number. A Rayleigh number criterion characterizes the convective instability of the cool skin under solar heating. Under low wind speed conditions, the solar heating can damp the convective instability, strongly increasing the renewal time and correspondingly decreasing the interfacial gas exchange. In the ocean, an additional convective instability caused by salinity flux due to evaporation becomes of importance in such cases. The new parameterization is compared with the cool skin data obtained in the western equatorial Pacific during the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment in February 1993. In combination with a model of the diurnal thermocline it describes main features of the field data both in nighttime and daytime. Under low wind speed conditions (< 5 m s-1) diurnal variations of the sea surface temperature due to the formation of a diurnal thermocline were substantially larger than those across the cool skin. Under wind speeds > 5 m s-1, diurnal variations of the surface temperature due to the variations of the thermal molecular sublayer become more important.