A broken thermometer gave me the chance to look at the temperature sensor.
Using a magnifying glass, I could see what looks like a glass bead with two clear contacts inside. It doesn't look like a thermistor. So it could be an RTD - resistance temperature detector. I hadn't realised there was so much to think about. I learned a few years ago about the relative merits of 2-wire and 4-wire probes but this article even includes 3-wire probes.