Or someone used a stop-leak treatment to hide a leak before you bought it... what coolant lines are you not getting fluid through? And how are you certain?
Confused at the”pump running when opening the door” comment. Door has nothing to do with water pump, but does with the fuel pump.
If the bleed screw snapped it needs to be replaced or you’ll have a leak. Fish it out and replace. GAS makes a nice brass option.
Going back to your original post, what exact code was given for the thermostat. They have a mechanical wax element so the fail open than closed most of the time, and a faulty yet open thermostat wouldn’t cause an overheat, it would cause an underheat. Things aren’t adding up; I think you have something else happening.
How long have you had this car, and has it ever overheated other than the time mentioned in the original post? A single overheat an a BMW N series engine can be catastrophic, it’s not an iron block ABA that can be ran without coolant until it heat seizes and then re-started a half hour later.
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