Our realtime thermal model for our giant TO247 fets is pretty simple: a capacitor to ground (thermal mass of the chip), a resistor (corresponds to theta from junction to heat sink) to a voltage (that corresponds to measured heat sink temperature). Calculated power dissipation becomes current dumped into the cap. The resulting cap voltage scales to junction temp. It's just a few lines of code.
We run that circuit simulation maybe 2000 times a second, and shut down the amp if it hits some effective junction temperature. The RC tau is about 100 ms, based on dramatic destructive testing of the real parts. Oops, sorry, elements. No, components.
Our NMR amps are current sources driving specific gradient coils. Customers program pulses or waveforms, so we can shut down and say "don't do that". Audio is not so controllable, so the shutdown would probably become some sort of limit there.