I'm not familiar with that particular model, but can give you some
info of how it works on my 1980 300SD, which may be helpful.

First, the aux fan only comes on rarely, during extreme conditions.
An example would be after hard driving in 85F ambiant temps, and then
suddenly coming to a stop and idling.   Or being stuck in bumper to
bumper traffic in hot weather.   So, if yoiu have an overheating
during more normal driving, it's not the aux fan that's the primary
problem.

On mine, the fan is controlled by a relay.   The relay in turn is
driven by either the coolant temp goiing above a certain point or by
the AC refrigerant temp going above a certain point.   When I've had
fan problems, it was either a bad connection where the fan motor
connects to the harness or the fan motor was shot.   The connection is
after about 2 ft of wire from the motor, which puts it in a bad
location to get road salt, etc.

Here's a simple test which works on my model and probably on yours
too.   I never needed to locate the coolant temp turn-on for mine, so
I don't know where it is.   However the AC overtemp thermo switch is
located on the AC receiver/dryer by the radiator.  There are 2 sensors
on it.   One is to detect low AC pressure, indicating loss of
refrigerant and to prevent the compressor from coming on.   The other
is the high temp turn on for the fan.   Assuming the AC refrigerant
system is working OK, you can temporarily put jumpers across both
sensors.   Then, with the AC on and the car running, the aux fan
should be running.   If it's not, then you know you at least have
other problems, eg connection, relay, etc. besides the engine coolant
turn on sensor.   There is also a fuse involved, so I would make sure
to check them as well.   Mine is located in the main fuse box under
the hood.

The auxilary fan is what you are talking about... in front of the radiator.
First, make sure that fan works by providing power directly the the unit.
The easy way to do this is by the AC dryer, there is a red or green switch
attached to the dryer, touch those two wires together and the aux fan should
come on... if not, remove fuse and check condition.

Secondly, that circuit is complex and is not just a thermoswitch that
triggers it. If you turn on your AC, it should come on immediatly. If not,
it is most likely you do not have enough refrigerant to trigger it. Too
little refrigerant will not trigger the aux fan.

The last thermoswitch is on the engine... should be two prongs blue color...
by pulling this out, fan should kick on high speed or simply on. This
depends on what car... some has two speed and earlier one like yours are
simply one speed.