Not to stir it up further, but lots of modern cars have a fiberglass mat glued into high stress areas such as trunk lids and hoods where they know people will be putting pressure on them.
Seems to me that the door is already disassembled, why not just fixed it with the traditional hammer and dolly method? Work the high area first to releave the metal stress and then start bringing up the low. I don't know much about heating and cooling method, but I'm pretty sure if the dent is large enough that it put an "eyebrow" in the metal, all the heat in the world won't help until that metal has been tapped down.