I have this exact problem in my E300D W124 - the fans switch on full when the engine is cold and the ambient is warm. They do shut off when the engine comes to normal temperature. But the relay clicks about 10 times in rapid sequence when it shuts off

The other bit I have noticed is that if the ambient is about 75 degrees - they dont switch on.

The blue temp sensor that goes to the HVAC PBU which actually controls the high speed function of the fans - shows correct resistance and when the fans shut off engine running - when I disconnect the plug to the sensor the fans work high speed just as they would normally.

I would have to dig into the dashboard to test the wiring and see whats wrong. Some people say the sensor goes bad and causes this while a dodgy PBU also causes this - but my HVAC works perfectly.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)