There's nothing that says that the property change of a thermometer which corresponds to a temperature change must be linear. All that is required is that the change can be calibrated and reproducible and a function of temperature. Monotonic would help, but I suppose one could keep track of small changes with constant monitoring devices to make sure that the reported temperature isn't discontinuous compared to previous values. One could also account for hysteresis effects if you're clever.
From: Phys-l [mailto:firstname.lastname@example.org] On Behalf Of bernard cleyet
Sent: Friday, February 2, 2018 12:38 PM
Subject: [Phys-L] thermometry
The current discussion on internal energy has me puzzled about the accuracy of measuring temperature depending on expansion. Is not expansion non-linear? Are expansion methods comparable to non-expansion methods (speed of sound- E-M radiation, etc.) comparable, because the the expansion is small, so a linear “first term” is “OK”???