Doing a bit of research, as mentioned by others the thermostat mostly fails by keeping the engine TOO cool.
Do you have the high instrument cluster and unlocked the OBC? I would monitor the engine temps via test 7 (or 9, I cant recall exactly which ATM).
As per various BMW forums the M54 runs at around mid to high 90's. Failed 'stats cause temps to be consistently at the low to high 80's from what people have reported.
Sometimes the classic symptoms of failed thermostats like long warmup or temp needle below middle dont show.
A lot of people do report poor gas mileage as a common symptom though. Not that it'll sip fuel like a Prius, but there is reportedly a noticeable diff.
