Thermostat is stuck open
WARNING: This page does not describe the selected car, but rather 10 other vehicles, including the 2010 BMW M6, 2010 BMW M5, 2009 BMW M6, 2009 BMW M5, and 2008 BMW M6. However, it is still accessible from the selected car via links, so may be relevant.
This figure 2 represents the malfunction-case of the system (thermostat is stuck open)
Due to the thermostat is stuck open ("stuck open" means, that the thermostat is not closed regular and a smallest opening leads to the same result as a fully open thermostat since there are no intermediate conditions), the engine coolant temperature (ECT) rises but does not reach the thermostat regulating temperature.
The coolant temperature model increases as expected without malfunction. The difference in-between the model and the measured sensor temperature is the criteria to set a malfunction.
As a result a fault code P0128 will be stored in the ECU.