yeah dude you have to rethink this
but all in all i do see where you where trying to go with this
if the box was made out of metal
and the sound proofing was made out of some type of fire resistant insulation
then and only then would this be kind of ok
you would proolly need some type of temp. switch so if it gets to hot the ballast would shut down , and even then it still would be a hazzard
and a waste of $$$
which would defeat the whole point of diy
at that point just buy a soundless ballast
not a bad cooling idea- except i wouldnt use cardboard
prolly do like a metal cool tube with the same intake outake (duct fans) and pipe out the heat or send it back into the house (its cold outside)