first of all, let me say that anywhere you can insulate...do so. My surprise was when I went on my first trip and found that the floor was ice cold. I had to go back and add more insulation under the carpet.
now, being that I used a commercial box, I didn't insulate between the skin and the studs. However, you made me think about that. I have built a few recording studios and looked at it from that direction. When we build sound rooms; we take sheet vinyl and wrap the inside of the wall before studding it out. This makes a sound barrier, not a sound absorber. This should work in the same fashion for temperature. Sound is basically the movement of air, so a barrier would also help stop the movement of air temperature. It makes sense in theory, right?
Doc Weaver '98 Freightliner FL60 pseudo toy hauler