Welcome!
I haven't ever cycled in the desert, but what worked well for me this summer when it was 103 F and humid was to fill a plastic soda bottle with water halfway and freeze it on its side in the freezer at work. Then, right before I rode home, fill the remainder with water. By the end of my commute, the ice was pretty much melted, but I had cold water for hydration and heat relief along the way.