i was at homedepot today lookin at the foam and sound board they carry but no one was sure if itd do wat im looking to do. im trying to find time to research pump house designs. but building an enclosure builds heat so i like the concept of doing sumthing like an airfilter intake system like u mentioned. ill have to def do sum more research and see what i can find.
A way around the heat is possible. If you do build a box, you can put a small 4" exhaust fan on the box, run the exhaust to your current exhaust system in a T. I also would get the insulated ducting for that exhaust to cut noise and heat offput.
For the sound, get the brown soundboard. I believe it is 3/4 or 1" thick. Double or triple it up. 1 board is around $10 and that would be enough. Also I suggest getting 1.5-2" styrofoam sheet and use that to build your box. Get the metal duct tape and make a box out of that. Then put the Soundboard around that. Probably soundproof then. The heat would be sucked out by the small exhaust fan.
The Styrofoam is pretty strong stuff believe it or not. I helped a buddy build a box like this for the back of his A/C and it has been working for over a year and holding up well. Costs less than $30 to build.
I hope this does help you.