At low temperatures, forward biased junction diodes make very linear thermometers. This is consistent with the ideal diode equation.
V = (kT/e) Ln (I/I0)
I = forward current, k = Boltzmann's constsnt, T = temperature in kelvin, and e = electron charge.
Here is a recent paper:
GaAs Junction diodes as cryogenic thermometers
Cohen, B.G.; Goordman, R.V.; Snow, W.B.; Tretola, A.R.
Electron Devices Meeting, 1962 International
Volume 8, Issue , 1962 Page(s): 74 - 76
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Summary: It has been observed that the forward voltage drop, at constant forward current, of a GaAs diffused p-n junction varies almost linearly with temperature from 2.0° K to above 300° K. Since carrier "freeze out", at low temperatures is not observed, these junctions make excellent cryogenic thermometers. In addition these diodes exhibit good repeatability on temperature cycling and an insensitivity to magnetic fields. The sensitivity of the devices measured near room temperature is Δ/VΔT∼ -3.5 mv/°C; If= 0.1 µA Δ/VΔT = - 2.0 mv/°C; If= 1.0 µA The sensitivity decreases slowly toward lower temperatures and at liquid Helium is: ΔVΔT∼ - 1.5 mv/°C and is essentially independent of current. This high sensitivity over such a wide temperature range is unique among cryogenic temperature indicators.