Which cooling fan are you talking about.  The cooling fan behind the
radiator in the engine compartment or the blower that is part of the
heating and air conditioning unit in the passenger compartment.

Can a mechanic wire the cooling fan of vehicle wrong?
I had my vehicle serviced for an overheating problem
and when I got it back it was blowing hot air when I
turned on my a/c? My a/c was working when I  took it in!
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It is possible that when the mechanic was servicing the
engine cooling system, he accidentally disconnected a
vacuum line to the AC air duct valve system.

You will probably get a better answer by identifying the
vehicle and describing what the servicing mechanic did.

Rodan.