I designed a couple of entertainment cabinets for a woodworking friend and what I suggested, and has turned out to be quite effective, is the following.
Along inside back top of the cabinet with the heat-generating equipment, place a series of one-inch holes drilled at the very top. A few inches in front of these holes, install a panel (1/2 inch plywood ?), either colored black, to disappear or match it to the interior color. This panel is installed at the top and drops down in front of the holes, kinda like a curtain. It should be long (high/tall) enough that the holes are not visible from the front.
In the bottom of the cabinet, under the equipment, drill another series of holes, which will allow air to enter from outside the cabinet.
The heated air will rise up inside the cabinet, exiting through the holes at the top and this heated air will be replaced by the cooler air entering from the bottom.
I have a very large entertainment cabinet which implements this method of cooling and I can leave the bottom doors closed and the equipment remains cool; well, at least cool enough to not cause a concern with overheating. In this section of the cabinet, I have four heat generating factories.
The best way to describe the effect is to think about those images of fire one sees on televisions or in the movies. You know?, those scenes where the fire is ?crawling? along the ceiling of the room in waves. The heat inside the cabinet behaves much the same way. The holes drilled in the top of the cabinet allow the heated air to escape. The panel hides the holes from view and the holes at the bottom allow the air into the cabinet to replace the escaping, now heated, air.
Think about it.
If I may offer another suggestion...
If you would like to hide the equipment, but still need to operate it remotely, consider placing an IR pickup in a ?rail or stile? frame member then run the lead wire of the pickup towards the interior and then split off the pickup signal and feed leads to all your equipment.
If you go this far, consider placing a surge protector inside the cabinet along with some A/V ?cables? that are easily accessible from the rear.