See, when one doesn't put their location in their profile, they get all kinds of crazy suggestions.
I have the perfect thing for you. Gulf Coast Sheep. They evolved for your climate in the southeast US. They developed bare bellies to shed heat.
You could house several in there. Meat and wool...
Very nice. Lots of potential uses. One would be, if you don't have any larger mammals, would be a brooding area for lots of chicks. Perhaps even a place to raise up some meat birds.
Do you have any livestock besides chickens?