I would recommend getting a cheap bluetooth adapter and the torque application. This will allow you to see what actual temperature is running.
Low speed fans should be programmed to come on around 216F and the high speed fans should be ~228F. Yes these cars are programmed to run a tad warm, however that temp on the gauge is typically much lower than you mention. Since gauges can be reporting incorrectly, I suggest the live scanning.
Also I would suggest looking at the coolant elbows, water pump and radiator for any obvious leaks. Ensure the system is full when cold.
