THere are many thermistors and they each have their own temperature-resistance curve. You could replace the thermistor by whatever you want as long as the resistance of the new component is within the range of the old circuit and you recalibrate for the different curve.
I think PTCs have a very sharp change in resistance with temperature though and as such are used more for current limiting rather than temperature measurement. NTCs are normally used for temeprature measurement from what I have seen because the change is more gradual.
THe thermistor will still change resistance far FAR more than a bad carbon resistor will over temperature though (even more than RTDs, the other resistive temperature sensor,...though that's not saying much). Like you would need a seriously bad, unstable, yet predictable resistor. I don't even know if they exist. You could try it though.