Engine overheating (or at least that s what the temp gauge says so)?

I m in FL and just bought 04 Honda Pilot, 115 k, a week ago. The a/c at the time of purchase seemed to work great. The weather here right now in January is obviously not hot, so I m not running a/c. However, yesterday I had to run a/c full blast because I had my dog with me, and then after five minutes, to my shock, I noticed the temp gauge go up to red zone. I of course pulled over and shut engine. I checked for leaks and coolant, and everything was fine and full. I tried running the car but the problem persisted. Got help from mechanic and we replaced thermostat and coolant, and pressure tested the system. Said everything should be fine. Drove for an hour or two and the temp gauge gearing up back to red zone.

What is going on? Is the gauge not reading accurately? Are my fans not working properly? Water pump? Radiator broken? Or something bigger than that? Did the mechanic miss something?

Thanks for any input!

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