Almost no matter how you do it, it's going to be a horrible waste of good drinking water to try to extract cooling from the temperature of the water. If you are in a dry climate, make a DIY swamp cooler. Otherwise shell out for a small AC unit.
Also; using your free lease-included water for stuff like that, is probably the quickest way to no longer have water included in your lease...
That's so on brand that I can't even be angry.