2005 vw jetta radiator cooling fan wont shut off

Truly a ridiculous amount of electronics in this vehicle. Lots of fuses and modules for radiator cooling, but no relay. That means it is a function of the ECM and the 'modules'.

https://www.autogenius.info/volkswagen-jetta-2003-2009-fuse-box-diagram/

In earlier models it is located under the coolant reservoir. Videos in the link.

https://www.google.com/search?q=2008+volkswagen+jetta+radiator+cooling+fan+relay+location

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I found this. I believe there is no fuse because the signal comes from the Engine Control Module.

https://www.vehiclehistory.com/questions/whats-the-2009-vw-jetta-fan-relay-location-289725

videos and images

https://www.google.com/search?q=2009+VW+Jetta+2.5.+Radiator+Cooling+Fan+Relay+location

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radiator fan won't shut off when car is off JoAnn, look in your manual for the cooling fan relay and change it, this is the problem in a lot of circumstances when cooling fan will not shut off(faulty relay). Check the attached links,instruction and guides, Good luck
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Thread Radiator Fan Won Stop
Symptoms of Bad or Failing Cooling Fan Relay

What fan? interior or radiator cooling?

Which Fan Radiator Fan?

replace thermo switch... this is normally located near radiator hoses.

Assuming engine tune / mechanical condition is not the cause of the overheating:-
Ensure cooling fan is cutting in at the appropriate engine temperature - check operation of the fan controlling relay,
Ensure fan switching control temperature sensor is serviceable,
Ensure cooling system is filled properly, taking care to bleed out air where necessary,
Ensure coolant pressure cap is of correct rating and in serviceable condition,
Check coolant hose on suction side of waterpump is not softened and collapsing at engine revs above idle,
Ensure radiator core is not blocked or cooling airflow inhibited by insects etc.

Locate your rad fan relay, and next time it does it, give it a quick rap with handle of screwdriver or similar weapon. If it stops, replace relay.

"Already had replaced: both cooling fans, fan control module, coolant temp sensor, fan switch, 4 terminal connectors. No trouble codes reported in VW electronic diagnostic test. 2 different VW dealers and and my mechanic threw in the towel. Any suggestions greatly appreciated."

This is a common problem with the VW..and no one has an answer WHY. (including VW mechanics)

THIS IS A RECALL ISSUE and should be implemented

most likely the relay internal contacts are burned closed, but this is usually caused by a cooling fan motor that is drawing excessive current from normal wear and age, so change both the relay and the fan motor.