we plan on filming after 10pm most nights -- we filmed the Klingon scenes, and it was all right -- we had a couple of huge blower fans to cool it off. We also have an industrial-sized airconditioner on that side of the house. We could open the door and lower the temperature considerably. But as hot as it was yesterday evening while we were working, it might be best to get an extra AC put it for a while.
PP, You do have a window behind the bridge set don't you? get a cheap-o window unit from Walmart, that way you can keep the set cooler.
Keep the AC up high during normal filming, then after the ship takes a hit or two, shut the AC down and let it get "warm". Adds to the look.
Nick Meyer used a similar idea when he was filming TWOK, he would have the AC turned off while filming the battle scenes, because he felt that the increase in temp, and the effect it had on the actors, helped the performance. If a ship takes damage, it's very likely that the air circulation system could go down or even seal off segments of the ship to prevent spreading smoke/toxins. That would change, during a high tension moment, does produce a physical response in humans.