The gauge is almost worthless. There's a place in the information where you can see the actual temp, on 2012 anyway. The gauge stays one notch below half from about 180-185 all the way to high 230s. The fan will run if the AC is on, and I believe it runs if you have defrost on. If AC is not on, the fan will kick on at 235. Somewhere around 240-245 you'll get a message that "AC is off due to high temp".
You need a way to get more info out of the car. The ultra gauge is convenient to leave hooked up all the time and you can make your own alarms such as high temp, but torque app have more information available.
Stock thermostat is about 225. You can use the guts out of a Volt thermostat which is about 180, but this won't solve your problem, just mask it/treat symptoms.
Edit
Passenger side is coming out of the radiator, drivers side is going in. I think your water is not flowing enough. Maybe clogged radiator. Maybe broken fins on the water pump if that happens to these cars...
Any gunk or any foreign material in the coolant? Mixed dexcool and old style green coolant?
/Edit
The gauge just started to move up here, at 240.
View attachment 299786