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Jan 10, 2016 at 20:02 history edited Transistor CC BY-SA 3.0
Added power non-linearity comment.
Jan 10, 2016 at 19:46 comment added Transistor Note that the constant current solution gives constant power per unit length which will be most useful for variable length cutting wire as indicated in your update. Wire temperature is only one of the variables. Foam material, thickness and cutting speed will also vary so you're going to end up with a table of values that work for you. Current control will probably be just as good as power / temperature.
Jan 10, 2016 at 19:18 comment added nagylzs Yes, constant current will give constant output power. It is must better than nothing, but I would rather have constant temperature instead. (When the thickness of the foam changes in time, the power needed for constant temperature also changes.)
Jan 10, 2016 at 19:13 history answered Transistor CC BY-SA 3.0