Can temperature probes go "kinda" bad?

I came to a beverage cooler that "wasn't cooling very well" and found the evaporator completely frosted/frozen up. (Compressor running, condenser fan running, no dust on coils, all door-seals good - usually means the thermostat/temp-probe is bad.)

When I put the temperature probe in a cup of ice-water, the digital temperature display wouldn't drop below 39°F while my multimeter probe was reading 33-34°F.

So the cooler temp probe seems to kinda work but not enough? The cooling deck never stopped running, so I'm thinking the evap is frozen because the deck runs and doesn't shut off because it never thinks the temp drops below 39°F.

So my question is: Might the probe be somewhat effective to read temp as low as 39°f but not effective enough to read any lower? I always thought a temp probe would work right or not at all. Could the digital thermostat be defective in a way where the probe might be right but the thermostat doesn't correctly output the real temp given to it by the probe?

Thanks.

submitted by /u/Quirky_Cauliflower39
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