Hmmm does the "the german" have VagCom aka VCDS? The ECT, G62, reports the coolant temperature to the ECM and to the dash gage. Now if the G62 is malfunctionnng VCDS would tell you that; I know my G62 was flaky for a long time and I finally replaced it. I am guessing the ECM must think the G62 is ok, and if the coolant temperature is low, well then it is the thermostat.
What does you dash temperature gage say? If it is low than I would still go with the thermostat. If not I would lean towards G62.
It is pretty easy other than figuring out what to do with all the coolant that will come pouring out. If you had the Bentley Manual for you car you would see how easy it is; or go out to your car, remove the engine cover, and look down below the injection pump.