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When trying to tell whether a thermostat, or thermal switch, in a refrigerator is truly working, one must chill that thermostat with (for instance) a piece of ice held to it, and measure with a voltmeter or resistance meter, as to whether the switch inside the thermostat has closed, when the thermostat is sufficiently chilled.
For instance, set the thermostat to the weakest setting it has without being disengaged or Off altogether: something like '1' on a scale of 1 is warmest, 10 is coldest.
Measure across the thermostat at that setting. It should be 'open' or infinite Ohms of resistance.
Then hold ice up against the thermostat for 5 minutes. Then measure whether it has closed, at which point it should read 'closed' or near-zero Ohms of resistance.
As for whether the defroster heater has failed to turn Off... A: the freezer would be quite warm if that were so! and B. the thermostat *would* try to turn On the compressor again and cool things off... provided the thermostat were *not* set on Defrost or on Off.
That could be done, yes.
If it is a standard unit, it has two terminals on it. Correct?