Ducati ST2 fan coming on randomly

Hi everyone,
I am at my wits end. I have a low mileage 2002 ST2. It runs very well except that the radiator fan comes on randomly. I have drained the system twice. The system is pressurising. I have replaced both temp sensors and there is no change in behaviour.

That behaviour is:
I run the engine and normally (but not always) somewhere between 145f and 165f the fans starts. I turn the engine off, the fan continues running for 10 seconds, and then I turn it on again after the fan has stopped, normally the engine temps will continue to climb and it will switch on again, seemingly randomly at any temp upto 195. I can then repeat the procedure to force the temps higher. I did take it to 230f and the fan did not come on and I lost my bottle. Once the fan starts running it continues running regardless of the temperature. The only way to stop it is to turn off the engine.

I would point out that I cannot get more than 2250 ml into the cooling system and that is all that comes out when I drain it. Not including the reservoir.

Any ideas would be appreciated.

In case anyone is interested a NOS ECU solved the problem.