I think I used a combination of most of the ideas here for my curved foam. I never used a soldering gun though.
I wanted 2" curved segment on my cabin.
I tried to heat bend foam and failed to bend pieces any thicker than 3/4". When I kerfed foam, it kept breaking when I bent it. I ended up shallowly kerfing (1/3"-1/2") 1" foam with this hot cutting tool.

This could be bent without breaking with a heat gun.
I glued together two pieces with the kerfed sides facing each other to give a nice smooth surface on both outside sides.

I am pretty happy with the way it turned out.
viewtopic.php?f=55&t=75248#p1297194I used a old "dumb" 12V battery charger as a power supply for hot cutting. Using ghcoe's idea, the length of the wire modulates the resistance and the heat of the wire. I tried some arbitrary lengths to find the right temperature.
They don't market these chargers anymore but maybe you could find one on line or at a yard sale. There are several web sites and utubes that show you how to make a DIY one.
Tom