I used a router that was mounted inside a box at a mantle factory I worked at once. The box was roughly 3 feet square and I could feel the heat through the walls of the box. For that reason alone I've never wanted to mount mine in a box. If you do, and quite a few have, you MUST have incoming fresh air as mentioned by David. The router's built in cooling fan is trying to push air from the box up and out past the bit so there has to be air to replace it. The intake holes in the box have to be at least as large as the area of the pipe sucking it out.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.