Got a 2014 regal turbo and its done this for a while with the fans but the temp gauge is a new one. The fans will run long after shutting the car off, like 2-5 minutes. Even if it is cold (currently high 30s low 40s). During the summer it would do this at the fastest speed and it was really loud. Now at least it's pretty low. It didn't do this when i first got it.

The new one is the gauge and what's currently leading me to believe it's a faulty temp sensor or maybe the thermostat. I could be driving and in the span of a couple seconds, the temp gauge will go from the one line under half where it usually sits up to just about the red then back. The other day i actually got the message on the dash that it turned off my ac because it got hot. It did this again today.

Ive had a lot of cars but only had one overheat and it didn't heat up then cool down anywhere near that fast. So am i on the right line of thinking that it's probably a sensor acting up?

Additionally... Where is that temp sensor on the ltg? I think i see it on the driver side near the thermostat but closer to the firewall but not 100% sure that's it.