If your current box has 4" of insulation and you took 2" off on all sides...
Say your current box insides are 24"x22"x24". Thats 7.33 CF.
If your "Thin Insulation" allows you the same exterior, even if you assume that you could take ONLY 2" off of the 4" (you can get more, but)... Your new box would have interior dimensions of 28"x26"x28" -- or 11.8 CF.
The power of cubing for volume.