Mine is from VanAlstine. It's easier to find a picture of it online. Mine holds razor sharp blades of different widths, and they get clamped into a heating element. On mine, the blade stays cool until you press the clamping mechanism (which holds blade) against the rubber. This activates a switch that energizes the blade (like a filament in an incandescent bulb). The razor sharp blade then gets hot and you push the tool as you follow the path you wish to cut. The nice thing about mine is that it is instant on/instant off. Mine has 4 heat settings, and I have yet to use level 4. I usually use 1 and 2, with 3 used for cutting fresh, 1/2" lugs into our 22. 5" tires.
It literally cuts like a hot knife through butter.
The regrooving "machine" you are thinking about uses the exact same regrooving tool that I have, except that the "machine" part is the part that holds the bare tire, or a tire wheel assembly, and slowly rotates tire forward or backward hydraulically. Since I do mine right on the truck, I just jack up the corner I'm working on and rotate it with my free hand, and hold it with my feet or knees.
I can insert u-shaped blades that cuts 1/32" wide up to 18/32", depending on what I need.
The thing I found most interesting is the consistency of the rubber. When I cut a strip that is roughly 1/4" x 1/4" and several feet long, I have yet to be able to pull one apart!! The rubber is WAY stronger than I would have guessed!
I think mine cost around $380, more or less. I knew I had a lot of rubber to cut, and this one is what the pros use. The soldering gun one works, just slower.