Like Ron says, “Seal Temperature Indicator Strips”! The dry mount press thermometers are not exactly manufactured to NASA’s highest standards.
It sounds like the thermostat is beginning to show it’s age. They are easy to replace (as long as you turn off the power to the unit before you begin - yeah, been there, done that!) and fairly inexpensive. It would be wise to change it before it goes completely berserk and melts 3/16” foam board to the thickness of a sheet of paper. (It is kinda neat when that happens, though – although explaining it to your customer is a little more problematic.)
I would suggest you get two replacement thermostats so that when this happens again in a few years, your down time will only be a few minutes rather than a week or so waiting for a replacement.
Both the strips and the thermostats (at least the SEAL brand) are available through United MFRs.