2000 Passat cooling fan running at startup

2000 Passat 1.8T Automatic with 80K miles.

Heres the setting: the first startup of the day, whether its morning, afternoon or evening, irregardless of whether the car is in the garage, or outside, or whether its cold or warm out. Also, the A/C, and the climate fan are definitely off, and were turned off before the engine was shut off last.

Problem: I'll start the car, and aux cooling fan will come on and run for about 30 seconds and then go off. After that, the cooling system runs completely normally, with the coolant temp guage never moving from the normal spot, and the fan coming on when its supposed to (sitting in traffic, a/c on etc). Additional startups during the same day dont cause the fan to come on. **The car was in an accident a few years ago, and this problem arose shortly after. It was my girlfriends car at the time, so who knows how long after the repairs this started.

Ordinarily it wouldnt be a problem, but the car has been doing this for a few years now, and the fan now sounds like a jet engine starting up. Im affraid its going to be an issue when I go to sell the car.

Does anyone have any idea what the problem might be??