Two things: The A/C gets excercised with request for defrost but shouldn't cool the engine down but explains the fan coming on. It would use the same relay.
The engine has a thermostat to allow it to heat up to temp no matter how much air is fanning the radiator. Sounds like the thermost doesn't close all the way for warm up.
If aux fan is aftermarket it could have been wired to come on with compressor on only not just when A/C is asked for as compressor will shut down when it's too cold anyway,
T
Tom Greenleaf - MetroWest Boston - USA
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