my approach would be 2 LEDs green and red. The green would normally be on and go out when close to overtemp The red would light on shutdown.

form a setup as the above, you do not need worry about linearity, just 2 setpoints.

I agree. And PTC shows rather sharp behaviour arround characteristic temperature. In combintaion with simple comparator or even a derivative containing anolog comparator performance can be implemented very easily. Make a voltage divider consisting of PTC and suited resistor and compare with fixed threshold.

While NTCs are better for temperature measurements over a large range, PTCs are better if you want to have some distinct or abrupt change of resistance at characteristic temperature. PTC are highly unlinear and cannot be used for temperature measurement over large range. That's the reason, why never curves are published. At least, I have never seen such curve for PTC.

Kai