thanks mariontr for the link, unfortunately it seems no RCM to sell there.

onehundread80 I try to answer
the fan start only when the engine is turned on, the AC is OFF and when I turned off the engine the fan turns off. no lights ON in the car. we also changed the Conditioning control module but nothing.

I can add some info more, for example I had a problem with a battery drain, a battery Bosch 2 years old but used really a little. then the fuel door was blocked and the mechanic needed to unblock. then the problem with the fan.
I read all the topics about this issue, in one of them someone unplug the positive pin of the battery for a couple of hours and this reset the fan. I don't know if it works, I didn't try it yet.

I love the Crossfire but I had really a lot of problems, all electrician problems and here in Rome it is really hard find someone who knows where to put his hands, Once I brought the car to the offial chrysler where the car was bought and they asked me around 700€ without fix my problem, better, the same problem appear again 2 months later.

I'm a bit embittered, thanks for all your help