The radiator fan does not turn on and run on after the ignition switch is turned off. There is no problem with the coolant temperature, i.e. it is not overheating. Today in my part of the world it was 35C and I had the A/C turned on while driving for over 50 km. When I stop and parked I noticed that the radiator fan turned off as soon as I switched off the A/C.
On my previous 1997 GTI VR6 the radiator fan will turn on for a few minutes after the ignition switch is turned off.