I have the same problem, but it's really only an issue in summer.
After about two or three hours in the theater room the temp goes up about four degrees. It levels off after that, and will only go up about another degree or two over the following two to four hours.
We keep our indoor temp at 68 degrees in winter, so that's not an issue. But in summer it can get close to 80 degrees, which is uncomfortable.
We have a whole-house air exchanger, so air is constantly moving in and out of the room, but that's only of limited value. It's also a bit on the loud side, so I turn it down to low speed during movie watching. The exhaust grill is directly above the projector, so that may help a bit.
There's always the option of a ductless air conditioner. They're supposed to be quite and non-intrusive.
Scott