Following along in this thread since my hens are to be for eggs and the occasional table bird. It's been a long time since I kept birds and never in north Texas. I farmed long ago near Bryan-College Station, near Texas A&M. And yes, I am an alum.
Seeing your question regarding rabbits in the south Texas heat made me think of cuy, aka guinea pigs. I've researched them as an alternative to rabbits for small meat animals. I'm 100% certain I'd choose them over rabbits. I'm 80% certain I'll start trying them for myself within the next few years. I've cooked and eaten them. Pretty close to rabbit, though more delicate in texture. They do fine in heat and also tolerate cold if managed properly. Google cuy if you are interested. If your Spanish is good you will have an easier time finding info. Cuy are a South American staple.
Good luck to you all. Thanks for sharing your experience.