As already stated, getting the heat OUT is a huge problem !
If I was going to attemt a project like this I would start with 1" aluminum foil faced polyiso foam. The corners can be large finger joints. Even with aluminum foil, you need a metal heat deflector spaced about 2"-3" off of the side where the exhaust exits and at least 8"-12" away from the muffler..
Heat and noise want to go up. If you make you box tall (5-6') you may not have to put a lid on it at all ! If that is impractical, mount a shorter box on 6"-12" feet on the four corners and mount a large fan on the lid blowing DOWN.
