"Would it be proper to say that: The kinetic energy that the molecules have gained in order to separate from the surface of the liquid is removed from the liquid by the departing molecules, in the process the liquid has lost the kinetic energy of the molecules and also the energy that caused the molecules to escape from the liquid."

You might be right, but don't think this would be significant in regards to water- water has large amount of latent heat:

"Latent heat describes the amount of energy in the form of heat that is required for a material to undergo a change of phase (also known as "change of state").
...
For example, in the atmosphere when a molecule of water evaporates from the surface of any body of water, heat is transported by the water molecule into a lower temperature air parcel that contains more water vapor than its surroundings. Because energy is needed to turn water into water vapor, water vapor is a way for a body to release energy."
http://en.wikipedia.org/wiki/Latent_heat

The significant amount cooling that water is capable of performing is related to latent heat
Gas molecules leaving gas molecules wouldn't have latent heat as far as I know- and as said it's probably related to water's molecular structure [gas molecules don't have structure- that's makes it a gas- though perhaps that's not quite right, you have a change in state from gas to plasma- and that might require a lot of energy].