@Wyleecoyote at the risk of you biting my head off, may I try and explain please?
Your kettle is fitted with a fixed thermostat. It senses the temperature of the water, not the room, then swithes off your kettle when the water is boiling. This works successfully at most altitudes although the boiling point changes slightly with altitude.
Your daughters hairdryer has a thermostat that senses the temperature of the heater. If the air intake or outlet gets bloked and the heater starts to verheat the thermostat will shut the unit off and prevent a meltdown.
Your wifes iron has an adjustable thermostat. The adjustment is by varying the gap between the thermostat contacts. It senses the temperature of the irons soleplate and switches off when the temperature reaches the set value, the higher the set temperature, the wider the gap and further the moving contact has to travel to operate, not the room temperature.
Your heaters work in the same way and sense the internal temperatue of the heater. As they are convector heaters this temperature will vary fairly quickly as you have rightly stated. Oil filled radiators work in a similar manner by sensing the oil temperature, but do it more successfully, the downside being they take longer to warm up and longer to cool down, but are much more effective. I use one in the greenhouse when I plant my spring seeds and it regulates the temperature very well.
Place a thermometer in your room and adjust your heaters and you will see that the room temperature is controlled, not very accurately but it does work.
I used to work for a company that manufactured bi-metallic thermostats and can assure you that the ones in your heaters are functioning exactly as the manufacturers intended.