Tas, one option would be to make a few 1-inch holes in the top and bottom of the cabinet, maybe along the back, and let convection provide the air flow. Of course, without seeing the cabinet, it would be hard to tell you exactly where.
When you said the cabinet "backs up to another room", I assume you mean that the back of the cabinet is exposed. If so, maybe a black-fiberglass window-screen material could be used.
If you mean typical kitchen cabinets, the uppers, being only 12" deep, you'd be limited to my first suggestion, unless the tops reach the ceiling. If you mean the lower cabinets, typically 24" deep, there should be enough air to not be a problem.
Then, there are the motorized options. one or two 3- to 4-inch fans set over similar-sized holes, again in the top, blowing out, or the bottom, blowing in, should be plenty. In either top or bottom holes, the fans should push the air upward Sometimes, with air holes top and bottom, fan(s) in a middle shelf work well.
Another thing you can do with a small fan is set it over the ventilation slots of your receiver (again, blowing up), even if in a closed cabinet, and it will provide a surprising amount of cooling.
Many people here suggest that DC fans are quieter than AC, although it is a generalization. A Radio Shack power supply would be a way to power the fan(s) selected. AC or DC, the fan can be plugged into a switched outlet for automatic operation.
Larry
www.fineelectricco.com