It might help you get more information if you'd tell folks what year, engine, and model you're talking about. Since I do not yet have that information, I'll tell you what mine does. By design, the aux fan will shut off when the engine is turned off. The aux fan starts at low speed when the A/C reaches a certain pressure. The aux fan will run full-speed when the engine coolant temperature reaches a certain point. Without looking it up, I seem to recall 105C being in the neighborhood.
You can find some repair information online at
http://mb.braingears.com/ and other similar sites, but I'd suggest you obtain the factory service manuals on CD or DVD if you're serious about understanding your car.
EDIT, I see the model as 300E, but details would still be useful.