Depends on the relative humidity of the surrounding air. At a relative humidity of 0 and an air temperature of 120F you can cool water to about 64F under ideal conditions (high air flow and small volume of water) through evaporative cooling. This is the principle behind a sling hygrometer where you have one thermometer with its bulb covered with a wet cloth and another that's kept dry. You then determine the relative humidity by looking up the two temperatures on a psychrometric chart such as:
http://en.wikipedia.org/wiki/Psychro...ometric_charts

While 64F water isn't really cold it sure feels much more pleasant than drinking 120F water.

I started using the wet sock cover on water bottles when living in Arizona. Water coming from taps in the desert was sometimes too hot to drink comfortably but we'd fill our bottles with it and soak the sock so the water would cool and be drinkable after riding a few miles.