Suppose I leave a glass of water on a table at STP. The water molecules at the surface of the water can be assumed to obey the Maxwell-Boltzmann distribution (at the least they obey a distribution of speeds comparable to the MB distribution). Only the most energetic molecules, near the surface of the liquid, have enough kinetic energy to overcome the attractive inter-molecular forces present in the liquid. As these highly energetic molecules escape from the liquid (i.e., evaporate), the average kinetic energy of the molecules in the liquid decreases. The temperature of the water is nothing but a measure of the average kinetic energy of the molecules in that water and hence the waters temperature decreases. This is effectively the mechanism behind sweating.
But now, if only the most energetic molecules were able to escape the inter-molecular forces and end up as water vapour, does this not mean that the water vapour above the surface now has a higher temperature than that of the water beneath it since the vapour is composed only of the most energetic molecules and the remaining liquid contains only the least energetic molecules? If this is the case, then surely it is an example of energy flowing from a cold sink to a hot sink? I realise this is impossible and so my thinking is definitely incorrect although I can't seem to build an intuition for why I am incorrect. All I can do is simply state the second law and tell my self I'm wrong. But that's no way to understand so if anyone can help me out on this issue it would be most appreciated!