If it were me, I'd install a small computer fan in the side wall of the cabinet and have it exhaust into the closet. I'm guessing that the opening between the door and the frame would be sufficient for air flow with the fan 'pulling' in air. If not, a louvered door would be the next option.
Here's an example -
http://www.radioshack.com/product/in...entPage=search
They are even available in 12V models -
http://www.radioshack.com/product/in...entPage=search