I've used cryogenic thermometers in my physics research, which IIRC were not thermocouples but basically calibrated chips of semiconductor, increasing their resistance at low temperatures. (Our usual temperature range went from 20 K down to 10 mK).<p>The trick with these puppies is to read the resistance without heating the thing up. We'd typically use a brief 4-probe DC measurement (4 probes so the leads don't contribute to the resistance), and inject a few or tens of nA, and read the voltage (in range of uV to mV).<p>Sometimes we used a lock-in amplifier, which is a pretty ingenius invention. You input a small AC signal, and then bandpass the output at the same frequency. That really cuts down on the noise at other frequencies, and lets you zero in on tiny signals from tiny currents with minimal heating.
I once wanted to measure the temperature dependence of some electronics component. Aha, I thought, I don't need no oven or such fancy things, I will just do my measurement while cranking up the room temperature, which I can record with a thermocouple!<p>I wondered why the thermocouple always returned to the same "room temperature" after half an hour or so, even though I and everyone else began transpiring heavily. It took me embarrassingly long to realize that the thermocouple only gives you the temperature <i>difference</i> between the two points of contact (tip and inside multimeter), and the multimeter took half an hour or so to warm up.