While driving temperature gauge goes to max hot with engine not overheating?

Can I ask if you have a check engine light on as well? If not you may have a bad instrument cluster (temperature gauge) which I have seen before. Here is how to change out the cluster which you can get a rebuilt unit by searching Google or Ebay. We should run the codes as well in case there is a code for the engine temperature sensor.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

The rebuilder will need the VIN number for programming FYI. Here is the location of the engine temperature sensor as well. Check out the images (below). Let us know what you find.