Forget dynamat and go for felt. Dynamat is good in making metal sheet sound "dead", it takes out all the vibrations of the thin sheet. Our cars are made from fiberglas, not steel. Therefor, no damping is needed.
Heat is firstly reduced by closing all the holes in the firewall as the engine is very hot. Then, cover the inside with felt. It is easy, cheep and give a luxury feel to the carpet.