Sorry, stepped away, this wasn't making sense.
Did a little reading, the thermostat is electrically heated. An electrically heated, DME controlled Thermostat is externally mounted above the cooling pump. The ECM (Engine Control Module) activates the thermostat to maintain engine coolant temp within a narrow range. If the electronics fail, the mechanical function of the thermostat acts as a failsafe to control the Fan and Electric cooling pump. You should get a check engine symbol in a full failure.
Once your car has warmed up please check and see if your RES heat works, this will tell us if your DME and ECM is functioning controlling and opening the thermostat to allow the coolant pump to circulate the heated coolant through the engine and heat exchange to allow RES heat, your fan should never run any longer the 10 min's after you turn off your car.
2008 X5 4.8i