If your box is hot to the touch with 3 CFLs, either you're using some very high-powered CFLs or you're not venting/circulating air in enough quantities.
I made a grow box out of an old plastic box of cat litter (scoopable) and the space is smaller than an HP computer case. I have four CFLs attached to it and it barely heats up.
Hope you didn't mount those CFLs directly to the case, that's a no-no and causes the case to heat up.
Speaking as a person that's ripped apart a Cray cabinet, NAS cabinet, and many Antec cases to make grow boxes.