I fought with one of these last year. New Wahler stat to replace the 3mo old Behr stat; no change.

Turned out to be a bad heater valve. Even with the heater off, I was always circulating coolant through the core. With the heat off, feel both outlet hoses, neither should be hot.

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12 E70 3.5i xDrive
03 E46 330i ZHP
01 E53 3.0i
98 E36 323is
12 Audi A4 Quattro
79 Triumph Spitfire
73 MGB