Measure it’s resistance if in a pinch. If it is in the kilohms range it is a thermistor. If it is super low resistance, it is a thermocouple. 10k ohms is the most common thermistor used in nearly everything consumer related. Nearly all common thermocouples are the same type too. It has been awhile, but IIRC they are k-type. The main difference in function is heat range. The thermistor is for lower temps and is less linear across the range in the cheap common ones. The thermocouple is two different types of wire welded at a junction at the tip. The heat causes a tiny voltage potential due to the different metals bonded together.

At scale of mass manufacturing, the thermistor is a fraction of a penny, while the thermocouple is a few cents. However the thermocouple requires an analog amplifier circuit to function, so this adds complexity in electrolytics. A thermistor is stupid simple and only requires a resistive voltage divider and any voltage threshold trigger circuit, so like a zener diode, capacitor, and single transistor.

The packaging of the sensor is the only thing you are paying for, and that is just for its mechanical mount and position, maybe some heat mass stability. A thermistor cannot handle direct flame temps, but a thermocouple technically can. In practice only the packaging of the sensor will contact a flame in some cases. Thermocouples are more rare but usually in any appliances that use natural gas. Thermistors are the third or third and fourth connection in most battery packs and found in almost anything with heat or temperature sensitive constraints.

In a pinch, all you need is the same sensing element. A coat hanger or anything similar may be a way to improvise holding it in place… should you ever need it.

The other type of common temperature regulation is a mechanical switch that uses a bimetal strip that deforms to close contacts. These will not work with the other two. Any device you hear a faint audible click from when heating, is using this type of temperature regulation. Typically old dumb coffee pots, clothes irons, etc. Thermistors are used in most small devices with some type of digital interface and a battery or heat.