The radiator fan only works when the air conditioner is turned on

Bsi error messages : Cooling function failure integrated in the engine calculator

Try changing the fan relay and any engine coolant fan sensor .Could also be the fan not operating on lower speed .

i changed fan relay ,other sensors and thermostat.
if i turn on air conditioner, radiator fan starting lower speed and car is not overheating all day.

How i check lower speed in a different way?

This explains how you can test fan operation .

" I've experienced an overheating problem, which I think is because of the radiator fan. The fan seems to work only on the high speed and no low speed. As far as I know it is supposed to be a 2 speed fan, because of the AC. I connected my car to Lexia and went on the Test options where I was able to find "High speed fan test" and "Low speed fan test". On the high test, the fan turns on and everything seems to be okay, while on the low speed test, the fan doesn't turn on at all. I can hear the relays(or some clicking noise) that activate the fan in both cases, but the fan only works on High. Also, there is an option which is "variable speed fan (chopper) test", and I can also change the fan type from the settings(there are 3types available - 1 speed fan(NO AC), 2/3speed fan(ac) and that's the one chosen by default, and Variable speed fan (chopper). When I change the type to Variable speed fan, the fan starts working and never turns off(even when the key is out and car locked), but the Variable speed test(chopper) seems to perform correctly - starting from high speed and then decreasing the speed."