I also don't quite think incorporating a fan into the design would increase it's efficiency. A quick google trip for PC Fan power usage gives me 1-2 watts for a 80mm fan. Small 5mm LEDs at 20mA and 3V should, calculated via rule of thumb, be at roughly 60 something mW. It just doesn't quite add up.

Evaporative cooling could work, but if you are planning on even including 20ml of cooling liquid, you could just as well put a CR2032 battery in there, which'll power the thing just fine.