I also installed four casters on the bottom of it, so it rolls around the garage easily. Last night I bought a small roll of reflective foil-based insulation:
There still seemed to be too much heat loss out of the front though, so I ended up sealing the front with the insulation as well, and cutting a small slot for the foam to slide in and out. Look, the Heat Box Monster is sporting a yellow tongue:
My box is only about 4.5 feet long, some of the longest hull-side planks need about five feet, hence the extra foam hanging out above. Not a big deal.
Closing off the front produced a dramatic improvement. After only about five minutes of exposure the part of the foam plank that was inside the box felt extremely pliable and soft. Almost too soft -- when I experimented with laying it into the mold, it was very easy to make depressions in the foam by pushing against it. You can also see that one end of the plank exhibited some scalloping: