And if it rises with rpm, that could be just be alternator output.Put a voltmeter on it and see what your alternator/regulator is doing from idle to 20 mph in whatever gear you were using in video#1.
That dash gauge regulator works by cycling full-on and full-off to create an average voltage, to power up the temp and fuel gauges. If battery voltage rises, so will the regulator output. The two gauges rising in unison is always an indicator of the IVR in action. And your IR gun is all the proof you need.
Now go put a thermostat in it before your engine-oil turns to muck.
