rad fan behavior

[George Nimmer]

I haven't been able to find any documentation which states the correct
behavior for the radiator fan in an '85 4000s quattro.  Here's what mine
is doing:

1. Coolant temp is high and radiator fan is running.  I turn off the
engine - radiator fan immediately stops.  Shouldn't it continue to run
until the coolant temp has dropped, even with the engine off?

2. When the car is first warming up in the morning, and coolant
temperature is starting to climb up to normal operating temp, the
radiator fan flicks on and off repeatedly sometimes, until normal
operating temp is reached.

3. The radiator fan is very loud compared to later model cars.  Is this
normal?  Is there a quieter fan from a late model Audi that will fit (or
that can be modified to fit) a 4000q?

Thanks all for your input.

George
'85 4000S quattro