If you access the temp setting in the instrument cluster before you start the engine, you can watch the temp fluctuation from when the thermostat opens and closes.
For 2002-2006 R50 Cooper and R53 Cooper S Hatchbacks, and 2005-2008 R52
Cooper and Cooper S Convertibles...
1. With the key in the ignition, but in the off position, press and hold down the
odometer reset button with one hand.
2. While holding the button down, switch the key in the ignition to position 1 (first
click) with the other hand. The screen will have a number and the word “TEST”.
3. Scroll through the numbers by pressing the odometer rest button, through to 19
and wait a moment. (Note: the number order is: 1,2,10,19)
4. The message will say 19 "L i-off", flash to "L i-on", and back to "L i-off" again.
When "log i-off" appears, press the odometer rest button again.
5. You are now in the system.
6. Scroll through to 7.0 Actual coolant temp.
Start the engine and go for a drive and you will see the Temp fluctuation as the thermostat opens and closes. Your thermostat should start to open at around 90.5 C
Don't forget, if your in traffic or at very low speed, you will have heat soak due to lack of sufficient air flow over the engine, on open roads at highway speed, normal airflow should be sufficient to cool the fluid in the radiator and again you wil see the thermostat open and close as required to keep the engine at its optimum operating temp.
Now, just to add to the confusion, the ECM activates the high speed radiator cooling fan at 122C / 251F which also activates the EHPS cooling fan (if fitted).
The Bentley manual does have conflicting info but you should be able to see where the average temp range is.