So, how much air needs to be moved, and how cool does the room need to be? I think that answer will help to inform the situation. To me this is a tricky problem if passive cooling is insufficient. Here's why:
At some point you have to trade air between some other volume of air and the air of your equipment room - the outside, or your theater. The problem with the outside is that the temp varies, and you're opening up to the outside.
Assuming you integrate the equipment room with your HVAC, is it better to add cool air to that space (supply), or remove hot air (return), or both? The problem here is controlling when this happens, so the easiest is probably to keep the equipment room the same temp as the theater.
I have a similar scenario with a slightly larger equipment room (8' x 3' x 14').
The difference for me is there is no means of exhaust outside the room - I can vent into the theater room near the HVAC return, into the ceiling joists, or into the space between the walls, and if this would work, I would simply dump hot air periodically with a temp-controlled computer fan.
My theater is a "room within a room", so it provides for some circulation of air (dricore floor, space in walls, space in ceiling joists). Also, the equipment room does not need to be all that cool, just cool enough so that nothing overheats.
My main motivation for putting the equipment in a separate room is to provide easy access to the equipment and some noise isolation, and there's not another space outisde of the room to provide for this. This is turning out to be more tricky than I thought.