For fresh air exchange they are generically called ERV and HRV. HRV is heat recovery ventilator. E is for energy and works for both heat and cool air recovery, which would be the one you would want. A bunch of companies make them - Trane, Broan, Panasonic, Mitsubushi, plus many more.
The problem is they're not very efficient, @ 70% top rated and actual performance suspected much lower for all of them. More efficient than an exhaust fan & a make up air duct on your AC ( which would be 0% ) but not exactly the silver bullet they sell them as either. I have 2 of the Broan ERV's and they bring in a lot of extra humidity in the summer time. If you have AC and it runs enough, it will take the moisture out, or you can get a dedicated dehumidifier. I have the latter because the AC in my basement doesn't run often enough because it's naturally cool down there. With the ERV on, the dehumidifier runs almost constantly and it creates a lot of noise between the 2 of them. The ERVs are fairly loud, much louder than my AC air handler, and closer to the sound of the vent above my stove. Also nothing works together, so if you're going to piece things together, give some thought how you'll control it.
Dennis did the plans for both LeBon and I, but LeBon's solution sounded better than mine. He had a humidifier that could pull in outside fresh air (but not exhaust stale air). That presumably would be delivered to the theater room to pressurize it somewhat. A portion of the air would be allowed to enter the equipment room through a dead vent. Then the equipment room would pull the hot air off the racks and vent that air outside (with a powered exhaust fan).
I'm not sure if he still plans to do that or scrapped the idea for some other reason. But to me, it's much more elegant than multiple AC supply & return vents in room, ERV / fresh air supply & return vents in room, and dehumidifier supply & return vents in room. I've considered getting rid of the Broans and getting going with LeBon's plan for both my theater & kitchen. The difficulty for me is the whole house is brick & stone with spray foam insulation, so not easy to cut holes in the exterior walls.
But to answer your question, yes, an ERV will pump fresh air into the HT and pump stale air out, while trying to recover some of the coolness & lack of humidity in the out going air. They typically have 4 duct connectors - inside fresh supply, inside stale return, outside fresh supply, outside stale return. You mount vents for the 2 outside ducts to a window or more ideally to the side of your home like a dryer vent. The Broan uses 1 combo vent for the outside air.
The other option I may try, which my builder recommended because it's simple... Attach a fresh air intake vent into the return air duct of the AC system. If an interior exhaust fan like bathroom fan, stove fan, or electronic rack fans, start to depressurize the house then fresh air is naturally pulled into the AC system, conditioned, and fed to the space through the standard HVAC ducts. There is a delay because the HVAC may not be running and no energy recovery is attempted, but it's like a $50 option, no electronics, no BS.