Read the temp coming out of the radiator see if it's making sense also the oil temp. With those two you should be able to tell if the thermostat is stuck open or the sensor is just whack. Also what does ECT read with scanner? Typically of they fail you'll get a temp like -40° or some crazy max temp. If that's the case def the wiring or the sensor.

New ≠ fixed follow the symptoms even if they point to a new part.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)