Bearly even if you use a thermal backed matting that covered the entire inside of the door, you will probably not feel any difference still if not only a slight difference. Insulation needs air pockets that are trapped to help slow heat transfer. This sticky tape stuff has no air gap so its thermal Insulation will be minimal at best. If you want to trap out heat wrap or dip your car white and get clear u.v. tint for your windows and windshield. That will help more than the sound deadening mat will (its only ment to stop sound not really heat)
There are drain holes in the bottom of th door skin that will let hot air in regardless of what you do and you never want to block those holes they drian water from inside the door.
