and that caused a "temperature is high" warning. Long and short, the turbo coolant pump was also replaced.

The cooling circuit for the intercoolers is separate from the engine cooling.105F is too low temp for a modern BMW engine.They use electronically controlled thermostat.The coolant temp in the city cycle should be in the 220F range and may go as high as 235F while cruising on the freeway.
And thanks for the link for the hidden menus.

105 degrees Celsius is
221 degrees Fahrenheit

I know ,but I am sleepy this morning ;) According to the BMW factory documentation the coolant temp on the freeway may be raised as high as 112C.

You wrote "105F is too low for a modern BMW engine". So it threw me off on your point.

If that's the case then it is imperative that the cooling systems have an adequate antifreeze mix. Water boiling at 210F and a 50/50 mix boils at around 265F (112C = 234F). My BMW idles around 225F at times. The thermostat opens at around ?? 195F ?? Has anyone tried a thermostat modification?

Yes,original BMW coolant is important,but dont forget the system is pressurized at over 20 psi,which is raising the boiling point significantly.
The ECU has a sensor on the radiator outlet hose.It will sense if the T-stat opens too early/at too low temp and will throw a code and CEL.