Does Arduino Uno R3 require cooling in a closure? I was looking at getting an enclosure to house my Arduino Uno R3, but I'm not sure if I should also attach a fan.  Does anyone have experience with this?  It doesn't look like much heat is being generated, but with no ventilation except some slits in the enclosure, there won't be much air circulation without a fan.  My concern with adding a fan was the fact that I'd need to power it.
The only times I had an AVR run hot was when I applied reverse power to it. You'll be fine without a fan for the Arduino board itself, as long as you don't run power hungry peripherals from it.

Probably the only thing you really need to check (apart from absolute maximum ratings: 40mA max per IO pin and 200mA max for the whole microcontroller) is the on board voltage regulator (usually three pin device with a heat sink soldered down to the PCB) if you power it from a voltage > 7V or so.