Like Vicious1 said, you can put baffles in the box to vent it. I actually read that the intake air that the vacuum sucks in should cool it. I wonder if maybe your filter is clogged, in which case you could build a cyclone dust collector, like this: http://makezine.com/projects/cyclone-dust-collector/
No idea if that would increase the sound and defeat the purpose of the enclosure though.
Good shop vacs don’t use the dirty air for cooling, that’s just bad practice. I’ll eventually get a real dust collector and put it in the basement.
Good point! Sorry, I wrote intake air, which would definitely be dirty. Exhaust air is what I meant to write, and I wouldn’t expect that to be any more dirty than ambient air. It was just a presumption based on something I read this morning that I can’t find anymore. Not meaning to be argumentative and I definitely wouldn’t leave a shop vac running in a sealed box unattended for hours on end in any case!