I'm wondering if you could make a field trip and do a rehearsal (or half a day? I suggest the latter half, when the heat would be worst) in a public park or something. Highly unusual and the company may just hate the idea, but if you've got a group who'd be into it (and in that kind of heat, a lot of people would be into it!), well.
You'd lose a significant amount of productivity (no props, no sets, no marks, etc.), but the stress level would fall through the floor, and there's something to be said for that.