My 03 GT has been having overheating issues for quite some time. The cooling fan will not run when the car gets hot, but will run if I turn on the A/C.
Yet, even if I run the A/C, the car overheats after about 10 minutes of city driving. When I turn the A/C on and turn the temperature dial to hot, that prevents overheating. But since I live in Florida, I need the car to run efficiently with the A/C blowing cold air. I've never had issues with the A/C producing cold air.
The temperature gauge works until it reaches halfway then does not continue to move past that point, even though I know the engine is much hotter.

I went to a local Ford dealership for a diagnostic test, where I was told I needed to replace the cooling fan assembly and that my battery was weak (perhaps this overall cooling issue is causing wear and tear on the battery?).

The cooling fan and thermostat were both replaced about 2 years ago when the car was overheating. The issue back then was a plug in that is located by the fan towards the passenger side (my dad is my mechanic, so I apologize for not knowing exactly what this plug in part is...).

I went to purchase a new cooling fan assembly from AutoZone, where the employee there talked me out of that and into buying a new temperature control sensor based on what I told him. I already replaced the CCRM thinking that was the issue before I brought it in for a diagnostic test. I disagree with the diagnostic test because in my understanding, the cooling fan itself works however the fan isn't receiving the signal to activate when the engine is hot. So to me that would mean it would be some sort of sensor or relay that is bad, but I very well could be wrong. But right or wrong, it just want it fixed!!

Any advice would be GREATLY appreciated!