< the resistance goes up as the temp goes up. So if it's unplugged, the computer thinks the engine temp is high, so it shuts down the compressor. Also, if the element inside an RTD breaks, it thinks the temp is very high.>

Just the opposite.
That sensor is a NTC [ Neg Temp Coefficient] thermistor sensor..as temp increases , R drops.
The open circuit is simply an Aux Fan Default from the ACC panel circuit.

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A Dalton