I helped a friend do the firewall and floor in his crew cab diesel once using something similar. I think the stuff he used was called BoomMat...? It was a $100 Amazon splurge for a whole roll and a roller applicator. Can't say much for the changes in heat (it was a black truck, so it was always hot inside thanks to the wide open western Oklahoma skies). However, it did lower the interior ambient noise a bit. Road noise and most of the diesel rattle well dulled out, but you can only do so much for the melodious 7.3 PS.
I would definitely encourage it on the flat vertical panels and doors just to add sound absorbing density and get rid of some of the tin can effect, but don't think that it's a cure-all. Most sound studies recommend a combination of MLV (multi-layer vinyl) plus a jute or closed cell foam to get the best sound and heat reduction.