After you have added the coolant have you bled the system? It's a simple thing to do and will release trapped air in the system. And yes, the coolant sensor is that sensitive...

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Current:

E92 M3 - Alpine White / Fox Red

Retired:
2007 650i Barbera Red
2007 750i Jet Black
2006 M5 Carbon Black
2002 X5 4.4i Steel Gray / Black
2002 M3 SMG Carbon Black
1997 BMW 540i Aspen Silver
2000 BMW 528i Jet Black
1997 Range Rover HSE
1994 Porsche 968