Soooooooooo. Is it possible that this is not a 2000 model year V6? For example a 2001 model year V6 uses a single speed fan.
Note, using a two speed fan in a single speed application would not have the symptom described.
If you want to answer the question about the temperature sensor an ODB2 scanner would make short work of your problem. Here's some information regarding an affordable Windows based unit.
ForScan ODB2 scanner w ELM327 USB
https://www.stangnet.com/mustang-forums/resources/forscan-odb2-scanner-w-elm327-usb.57/
And yes part of the CCRM is the fan controller. But think about it for a moment. If we assume that your car has a single speed fan AND the cooling fan runs when the AC is on, THEN the problem couldn't be in the CCRM.
Again having an ODB2 scanner that is capable of monitoring operational data would take a TON of guess work out of the trouble shooting.
I'm also assuming the fan connector itself is in good repair with no signs of over heating or dirty connections. Here's some information on how to confirm the voltage to/from the fan.
Howto perform charging system voltage drop test
https://www.stangnet.com/mustang-fo...perform-charging-system-voltage-drop-test.56/
Final note, IF you have confirmed voltage at the fan plug and the fan still isn't working look at the fan itself. Think for example worn bearings. Why is this important? Because in single speed applications the fan is protected by an automatic resetting circuit breaker (CB). This could explain how it's possible for the fan to appear to come and go.
Question: When does the motor over heat? During stop/go driving? Long expressway trips?
If the motor only overheats during stop/go driving and maintains correct temperature during expressway driving my educated guess is the cooling fan is drawing too much current and tripping out the circuit breaker. Why? Because the fan is not needed when the car's speed is above 45 MPH.