Need help with long Distance 3.0T overheating diagnosis

ok, got a call from the wife. I won’t be able to look at the car until tomorrow.

She got a high coolant temp. Warning turn engine off message.
Temp gage was far right on high.

She pulled over. Opened hood, coolant level in the overflow tank was correct just below max.
Engine compartment did not feel hot and no coolant was leaking.

Ten minutes later she started the car. The gage was at half. She turned the heater on full. She could drive about 5 miles before the gage it went up to 3/4. She pulled over opened the hood no coolant and she could touch the cylinder head it wasn’t too hot. She waited another ten minutes later the was able to go another 5 miles to get home before the gage climbed to 3/4.

I live in Florida it 80 Degs.

My thoughts:

  1. If the car was overheating, it would not have cooled off to 180deg, half way on the gage in 10 minutes.
  2. If the car was overheating, she would have felt a lot of heat when lifting the hood.
  3. If the thermostat was stuck would she be getting hot air out of the heater core in the car?
  4. My buddy is pointing at the temperature sensor, I would think if the sensor was bad it woulding be climbing consistently to hot it would be more irrattic.
  5. My buddy says when I get home to read the temp sensor output and the radiator outlet temp. Compare them, if the radiator is staying at 190degs but the temp sensor is hot then it’s the sensor.

Any additional troubleshooting or suggestions would be appreciated.

Thanks
Ed