How to measure temperature of a syrofoam cutter hot wire?
Because your supply is unregulated, you can try something like






simulate this circuit &ndash; Schematic created using CircuitLab

Using a current sense resistor (in this case, 3 0.1 ohm power resistors in parallel), you can find the current through the wire. Then, knowing the voltage across the wire you can divide the voltage by the current to get the resistance. Referring to a table of resistance for your wire, you should be able to derive the resistance and hence the temperature. Nominal current voltage will be about 0.27 volts, which is a fairly convenient voltage level to measure, and a x10 amplifier using an op amp should be simple enough if you need it.

For the setup shown, 3 5-watt resistors could be used, since the nominal dissipation for each resistor is about 2 watts. Heatsinking the resistors will help accuracy.

While this is a sort of roundabout way of measuring resistance, it is arguably simpler than interrupting the heating cycle to make more conventional resistance measurements.