Driving down the road and all of a sudden on my display reads, air condition turned off due to high engine temp. My heat gauge reads almost hot. The display then reads normal, speedo on. The temp gauge goes back to normal. Like all of this in 30 seconds. This happened 3 times in a maybe 10 mile ride. What could it be. I know my car was not overheating. A sensor?

The display says the AC is turned off because it’s too hot. However, it says this when I first start the vehicle. The fan also immediately starts running, and when I turn the engine off after driving, the fan stops, it doesn’t continue to run as if the engine is overheating. I have no signs of the engine overheating.
The temperature gauge constantly stays at C, it does not ever deviate away from it. I checked my radiator fluid and it was dry. I filled it up and it is at the same level and hasn’t moved since which was about 10 days ago.