Our RIR's didn't do well in the heat here - we have humidity instead of a dry heat - it's really the humidity that does them in.
My friend lost all her RIR's roo's to the heat too this year. You'll want smaller birds that do better in the humidity unless you want to have a swamp cooler, or AC in the chicken house for them.
Our heat indexes in a lot of area's of texas, especially closer to the coast, will hit 140+ even in the shade.
I wasn't sure if Texas got humid or not and I don't know what breeds do well in humidity. Do any chickens? The dryness is one of the only good things about arizona. And it gets 140 degrees in Texas!? I don't know how you or the chickens can live in that. I lost almost my whole flock last year when it was 120 degrees. It was before I has installed misters. This year has gone by much better with misters and constant water checks.

Especially in a large group.
. So I I have mixed feelings about Rhode islands and probably won't get them again. I saw where you where you were thinking of putting misters in. I really recommend them. Going out and spraying them down so often really is a pain. And the only reason my new flock is still alive is because of the misters. I don't think they would have made it either if I hadnt put them in.