there should be a water sensor/sending unit on the intake somewhere in the water passage.
for air you can usually just runn it for a while with the cap off and it should burp out. then you may need to add coolant accordingly.
i would think he air is most likely the problem. whenever an air pocket gets by the sensor it is causing faulty readings.
Yup, air bubbles or a possible broken sending unit wire are the most likely causes.
Sounds like air, I had this issue 2 hours ago, with engine cold, open rad cap, and rev engine a few hundred RPMs higher than idle, hold it there till the temp gauge settle. Add coolant/water as needed Good luck