No, this is one of those oscillating thermostats.
This thermostat cannot accurately know grill temperature, because it is very difficult to get grill heat (transfer) to the bi-metallic switch. You need metal to conduct the heat between grill-thermostat but you also need insulation (electrical) which does not transfer heat well.
So instead, I have seen some cookers/toasters use a scheme where the thermostat incorporates a tiny heater. I see that in your pic. Wait, is it open-circuit, I see a break?
The thermostat+tiny heater is supposed to match the grill's thermal characteristics, like it is modelling the grill+big heater thermal response time.
I'm not sure what the carbon-slug does, if it's a resistor for the tiny heater.
So there is positive feed-back, this entire thing oscillates and here it sounds like the tiny heater puts out too much not enough and after a few minutes the thermostat thinks the grill is very hot when it actually is not. I'm not sure, I don't have success finding the adjustment/calibration screw on these.