You're in Vegas? I'm in Phoenix. Misters! Don't let them soak everything, you need to keep the coop itself dry. I have a stand mister and a box fan and it works great! My flock enjoys it a lot, especially in the afternoon. They lay on the wet ground and let the mist settle on their bodies. That and the cool water for wading are their preferred cooling off options.
Your coop needs a LOT of ventilation in our climate. You can help this by leaving windows/doors open and having a fan draw/push air through. I would get rid of the rats and mice first though. You can use poison in those little box things, Tom Cat or some such brand, away from your coop and run once you make it secure and that will keep those buggars gone.