I also got time to try my polystyrene cutter. 20 cm of 13.77Ohm/meter nichrome wire will cut polystyrene slowly with 3V across it. So that's about 1A, so heating is 3W. If you compare that to a low powered soldering iron of 10 or 15W I suppose it sounds about right, but I might try different voltages and see if I can get a faster cut.