Originally Posted by raceyBMW
It depends on how they fail, if it fails open, or gets stuck closed
Lets assume they fail into an open position though. That means you will have coolant flowing through your radiator at all times, should be easy to check by feeling the upper coolant hose just after a cold car is started and seeing if there is coolant flowing (there shouldn't be if its working and the car isn't at operating temp)...you could even pull the upper rad hose to see if its flowing.
To check if its failed closed, when the car is at operating temp, check the same upper rad hose to see if you have coolant flowing through it or not. If it has failed closed, you will have no coolant running through that hose.
Just to note: According to the Bentley repair manual, the T-stat fails safe in an open position only so as not to overheat the engine.