How do you hang your lights? are all your CFL lights at the top of your grow box?
If yes, then there might be a way. You can try using a glass shield to prevent the heat from your CFL lights from coming down into your plants. The glass shield will let light past through it but will keep most of the heat from getting down to your plants.
your grow box is what 2x2x4?, so Iam guessing a glass shield of about 2x2 should be enough. Install the glass shield about 1" below your lowest CFL light bulb.
If you dont want to use glass, you can use a plastic called "LEXAN XL10" its made of plastic, but very transparent, it has 88% light transmission. You can buy it at home depot, they have it in various sizes, I think the smallest is 11"x14" and it costs about $8?
If you want to know what this LEXAN XL10 looks like.
http://www.piedmontplastics.com/html/prodname-LEXAN_XL10_Sheet-350.htm
Intalling a glass shield is easy. Just go to micheals or a hobby store and pickup some thin peices of wood, 1/2"x1/4" that is about 24" long. Drill small holes on both sides of your grow box and mount 2 peices of wood there one on each side, you can also tape it if you want, the Lexan XL10 are light. the Lexan XL10 sheet will now have something to sit on.
The Lexan XL10 glass shield should be able to bring the temps in your grow box down by 10F, Iam assuming you have a fan exhausting the hot air from your lights.