In principle, it will be the heat flux (for evaporation) and the bulk air moisture concentration that governs the evaporation rate/interface temperature. At equilibrium, and in lack of any heat sources in the wall/water, the heat must come from the passing air. Hence, q''=h_air*(Tbulk-Tinterface)=m''*h_fg , where h_air is the heat transfer coefficient, m'' is the evaporating mass flux and h_fg is the latent heat of evaporation. The vaporizing mass flux is determined from mass transfer (see any good textbook a la Incropera, Cengel etc), where the interphase vapor concentration is linked to the (unknown) Tinterface as being the saturation pressure (or concentration) at that temperature. I think there is a section describing this procedure in the last version of the book by Incropera, deWitt, Bergman and Lavine. So, with regards to your question: The interphase temperature can be controlled by either controlling the heat flux (e.g. air temperature) or the mass transfer driving potential (i.e. the incoming air moisture content).

Good luck!

I reckon a variation in humidity (water density in air) would trigger the osmosis diffusive motion tp occur, driving water particles from the more dense (humid) area to the lower dense (dry) area. This max-exchange could promote heat transfer if the particles diffusing were specified to have a certain temperature.

Humidity change is related to temperature. Hence heat transfer has direct relationship.