Ok, I did some further checking on my own, and I found out that it's most probably not the fans causing the charging to stop - I ran the car for some time, the fans went on, the voltage dropped from 14.25 to 13.86 and after a 1-2s it went back to 14.15. Turning on the lights drops the voltage from 14.25 to 14.10, still ok I think.
Further - turning on the AC with the fans unplugged gives a voltage drop and the batt lamp goes on.