Depends on the type of thermometer. Most physical, mechanical ones operate on the principle that hot things expand and cold things contract, taking advantage by having something move on this principle.
Old types with the line that rises upwards though a glass tube as the temperature increases, the fluid was usually mercury and there’s a reservoir of it at the bottom. As the temperature goes up the fluid expands and has nowhere to go up but up the tube, and we mark off what the various heights mean. When it gets cold it contracts and gravity pulls it back down.
Thermometers with dials that rotate to point to a temperature are made with two different metals attached to each other, and coiled. Each metal expands and contracts at different rates, which cause the coil to get tighter or looser depending on the temperature, making the arrow move as a result. Add a hinge to the needle, anchor the other end of the coil, and you have a thermometer. These were common in heat/air conditioning controls because you could also have the moving part operate a switch to turn the heater or AC on and off.
Electronic, digital thermometers usually work on the concept of resistance. Some materials act as an electric resistor whose strength varies by temperature. Send a known voltage in one side, and measure the voltage out the other side while still allowing some power to flow. The voltage on the output side will correspond to a temperature you can report.
This list is by no means complete, but are probably the most common you will see.
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