I built one when I was about 14 yrs old. I used a very thin piece of nichrome wire, a doorbell transformer, a 10' extension cord, a 30" piece of 1/2" x 1/8" bar stock, a few screws and a few pieces of wood.
I cut the socket end off the extension cord and wired it up to the primary side of the transformer with a light switch. I built a platform out of some plywood
and 2x4s and screwed the transformer to the underside and the switch to the side. I ran one wire from the secondary to a short screw on the underside of the platform near the center and drilled a very small hole in the center. I attached the nichrome wire to the same screw and brought it up through the hole.
At the rear of the platform, I attached the 1/2"x1/8" bar stock to the underside of the platform with a couple of screws, one of which had a wire attached to it going to the other side of the secondary. I drilled a small hole in the other end of the bar stock and bent it over so it was about 10" or 12" above the top surface of the platform and the end was directly over the hole in the center. I attached the short piece of nichrome wire to the bar stock so it was straight up, and tight.
I fired it up and adjusted the heat by lengthening or shortening the length of the nichrome wire by simply wrapping it around the end of the bar stock. It worked great for cutting foam, styrofoam, etc until the fire marshall came by and confiscated it from my art class because it did not have a UL certification
Most foam shops use a Bosch cutter
with twin blades, like a long, two bladed jigsaw. If you have an electric
carving knife, you might be able to get similar results from it.
The last time I ordered foam, they cut all of the intricate pieces for me, at no extra charge.