While drawing out my projector box design, I decided to go with a hush box and add a 4" inline fan to get the heat out of the box and room. There is no return for the basement's HVAC loop in my theater room, just two supplies, so I thought I'd make use of an unused 4" duct that we ran during construction that was supposed to be for the equipment room (it kept overheating, so I added a ductless minisplit just for the equipment room). I'm going to tap into that 4" ducting in the equipment room, install an AC Infinity S4 inline fan on the ceiling of the equipment room, and then feed a new 4" duct through the soffit to the top of the hush box. In the pic you can see the hole where the flange will attach at the upper front of the hush box.
I rigged up a small relay box with a 120V > 12V power supply that powers a time delay relay. The logic is: JVC NX7 projector's 12V trigger powers on/off with the projector, turn projector off and the 12V trigger turns the relay and duct fan off, but the time delay on the relay will keep the power outlet for the fan hot for another 15 min to evacuate all of the hot air. Built and tested today and it works perfectly.
The hush box is going to hang from the ceiling in the back of the theater. I built a mounting plate with cutouts for the AV conduit box, 4-gang power outlet and the 4" ducting. Went to attach it to the ceiling last night and found out that my drywall guys are complete garbage - the ceiling had a bow of over 1/2" so the mounting plate wouldn't lay flush!!! Still fuming...... Not sure what I'm going to do, but it might involve brute force, hoping that it doesn't F up the drywall finish on the ceiling... (there's a big piece of 3/4" ply above the drywall mounted to the soffit framing).
Right now I'm building the lower box that will slip over the mounting plate's flange and attach to it with some #8
screws. As soon as the lower box is done and ready for paint I'll try getting that mounting plate mounted up. The back of the hush box is going to be held on with magnets and have a perforated aluminum grill to allow fresh air to be pulled through the hush box.