Sorry. That's not quite what I meant.
Water will evaporate at the surface (pretty much irrespective of temperature). The water vapour will diffuse into the rest of the volume of gas until it equalises. In an entirely closed system that would mean that eventually you'd get 100% saturation. But the actual equilibrium will be considerably below that because there are sinks of water vapor. The temperature dependence is not in how much water enters the system from evaporation, it's in the position of that equilibrium. Pumping additional water vapor into the system won't affect that equilibrium point, it will just affect how you reach it.

It'll have local effects on the weather of course ... you'll probably get much prettier clouds above cities.
( Dr. Shambolic je suis charlie, Wed 27 Aug 2008, 10:33, archived)