In a previous post I talked about wearing cotton in hot deserts (see Cotton for the Grand Canyon). Now I would like to point out that in the Arizona desert beginning in September, you should carry a survival blanket and a lightweight polyester fleece shirt or jacket (and maybe even some silk-weight long underwear) if you expect the nights to be cool or if you are hiking to higher elevations. Then if you are unexpectedly delayed or caught out after dark, you can switch out of your cotton shirt and/or wrap yourself in the emergency blanket. Or you might want to dispense with the cotton and wear nylon shorts or pants and a short-sleeve polyester shirt, but when you expect the nights to be cool always carry an emergency blanket and an extra layer of clothing.
In the Phoenix, Arizona, area the nights can cool down substantially even in May, especially out in the desert, away from the city asphalt and hot cement.