Right now, I have a modem, router, POE switch, and NAS drive in this closet. The door is closed all the time. The door gap is all there is for air in/out. The ambient is 72F outside the closet. When I open the door, I would estimate the temp inside the closet, at face level, to be around 90-95F. I should get a thermometer in there and get real numbers. Once I add an AVR, Tivo, Xbox, C4 processor, etc. to the rack, it is almost certainly going to require active ventilation.

I could easily put a passive vent through the wall behind the rack. That connects to the laundry/mud room, which also has a vent above the door to the rest of house for pulling return air from that room. Being that the laundry/mud room is a rarely used room, maybe it would be fine to use a fan to force exhaust air into that room vs. the attic. But in my mind, pushing hotter air back into the living space is worse than pushing conditioned (cooled or heated) air into the attic. But I am not an HVAC engineer, so I could be off.