FSR/FSU does not, according to any wiring diagram I have, control the AUX fan. The FSU controls the blower fan for heat/AC. (The fan blows air into the cabin.) The FSU controls the on/off/speed of the fan.
The AUX fan is in front of the radiator and blows air through the radiator to cool it. It should be on with the AC and may run for a few minutes after the engine is switched off. both the relay for the AUX fan and the AUX fan motor are known failure points.
There is an old post on the subject of cold one side, hot the other. It might be worth searching for it and seeing what Weasel and others said in there as to the cure for the problem.

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