2000 a6 4.2
is a switch , fan or control unit ?
is there a way to find out?
also car heats up

There is a thermoswitch for the fan.

http://www.audiworld.com/tech/eng.html
I am trying to look at this one and check if my motor work

It's unusual for the aux fan to not run with the AC on.

<a href="http://photobucket.com" target="_blank"><img src="http://i79.photobucket.com/albums/j137/maciunast/DSC03296.jpg" border="0" alt="Photobucket - Video and Image Hosting"></a>
thats the fan I am talking about I have this car for 3 months and I know it newer worked
<a href="http://photobucket.com" target="_blank"><img src="http://i79.photobucket.com/albums/j137/maciunast/DSC03297.jpg" border="0" alt="Photobucket - Video and Image Hosting"></a>
and wires so how can I check if motor works

the temps shouldn't climb much with the hood open and the primary fan running properly. I wonder if you either have an air pocket in the cooling system, causing the gauge sender to read high, or causing the fan sensors to read low. The belt driven fan works off of heat from the radiator, so it either doesn't work, or, it's not hot enough to turn on.

to test the motor, just apply +12v to the RED wire, and -12v to the BROWN wire, on the side that leads to the fan. Ensure that the fan blades can turn freely before you do this.

Connected fan to the battery and it doesn't work
belt driven fan works fine
so maybe you know were I can get it cheap:)
Could be the cause of heating up old thermostat or water pump because car has 90k
And water pump is making clicking sound on 1000rpm something like trrrrrt
This weekend I am going to change both belts water pump thermostat tensioner and both rollers so I want to include fan also