Hi - I am in the Phoenix, AZ area.
Have had chickens for more than 10 years. Mine are loose in the back yard so they can pick where they can get. I find them under bushes a lot. I will flood a depression in the shade so that they can stand in mud. My chickens seem to prefer this over a mister, which they avoided.
I currently have just one Easter egger, and a sex-linked, both hens. We had an accident some months ago and I lost all but my remaining Easter egger. The sex-linked was a cull from a commercial situation; I got her so the Easter egger wouldn't be alone. I am hoping that the Easter egger will go broody as she has for the past few years and I can get her a couple of chicks to raise. She has raised 2 batches of chicks for me and is an excellent mother.
I used to worry a lot about the heat but with shade, water, and mud to stand in, they do well.
my chickens prefer mud too. especially silkies.