I've experienced this issue on the 2003 E39 530i.
For me, the problem occurs when driving in slow traffic (5-10mph) for 10-15 mins. It also happens if I keep the car running in Park position (so the car is not moving) for about 5-10 mins. This usually happens at low RPM, ~1000-1500.
The fan start spinning violently and I hear the noise inside. From outside it is very very loud like a huge truck.
I do not experience these loud fan noise when driving at highway speeds (60-80mph). May be because fan noise blend into other highway noises.
The temperature gauge does not fluctuate. It remains normals.
I purchased the car used with not much history. I do not know if the previous owner replaced radiator or waterpump.