Too complicated, my cabrio didn't come with A/C.
A/C was installed here by a large company that does not exist anymore, it works on 4 relays that control the fan/compressor etc. units.

Problem is, the radiator fan started to work without a stop when the car is cold and off.

I want to check the radiator unit first that controls the fan.
If I connect the 2 wires (+-) together, fan starts to work.
If I put them back to the unit, fan also works but car is off

Can a bad unit cause that?

Does the fan come on if the A/C is switched off. I know that the fans come on in my Jag when the A/C is switched on, even if the engine is cold.

Yes

Engine is off! no key in the ignition.

Here is a how the system looks like (relay number 4 controls the fan unit):





4th relay:



Blue and yellow wire goes to the fan/radiator unit (yellow is the +)



When I take off the blue wire from the relay housing which is number 87, fan stops to works.
I've tried another relay and problem is still the same.

My guess is that the fan is switched on the earth side (the blue wire) and is earthing out somewhere on its way to the fan motor.

Bought a new fan unit today and problem solved!

Well of course there's gonna be something else.
I got a 62c-87c unit and fan always worked.

Got a new fan switch which is 87c-92c but once the fan kicks in, it never stops.
Only if I stop the engine, it turns off after 1-2 min.
Temp is almost below half. so temp is ok.