Overheating - A/C Fan Not Turning On

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2003 Mazda Protege5
So, just now, I was driving my car home for lunch and my temp gauge starts rising...and I can feel that the A/C is not blowing cool at all, though it's been turned on. I switch over to heat, blast the hell out of it and luckily make it home before my temp got in the red. Turned the car off, let it rest for a few minutes, and went to inspect everything...no leaking coolant, no cracks in radiator, overflow tank looks normal...I go and turn the car over again, everything starts up, temp is normal and the fan has kicked on. I turn on the A/C, temp starts rising and the A/C fan DOES NOT click on. Turn the car off. I inspect both fan fuses (30) and they are both fine, but I blow em off anyway and switch them, just for giggles. Turn the car on, and the first fan kicks on as it did before...click the A/C on and the A/C fan turns on this time...temp remains normal.

Left my car at home, didn't wanna risk anything, but surely there is an underlying problem here? Electrical? Wiring? I've posted in the past that the pulley on my alternator (which runs one of the serpentines) has been borderline going out, as the belt squeals from time to time, more so when I have a lot of loads turned on in the vehicle (i.e. A/C, headlights, radio) - I've gathered that I basically need to replace the alternator to fix the squeal and get solid tension back in the belt, since it's the alternator pulley that is messing up. Been trying to avoid this repair, as it can get pricey. Is the alternator the culprit here?

Thoughts?
 
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2003 Mazda Protege5
Sorry for starting a new thread, search function was not working for me...finally DID start working and commented on a related thread - can't figure out how to delete this one?

MODS PLEASE DELETE MY THREAD! THANK YOU!