i will try to keep short , but many (archive)

thoughts occur.
my daughter , older than yours, did similar thing. why don't they look at temperature gauge? they are so concerned about the gas gauge.
$400 seems much to high to charge you for the diagnosis. i don't mine personally to pay half hour or hour diagnosis charge if i don't do the work at that garage. maybe they are charging for compression tests.
do not feel obligated to leave car at the 1st garage to which its towed. call a tow driver and gladly pay him to take elsewhere for more estimates, after you have called that other garage. also, once that you are convinced of the damage some shops will give you telephone estimates.
sorry, i don't know bmw repair cost. my daughter's car is an older madza, with typical blown head gasket symptoms including very rough running and overheating. repair cost at my favorate AAA garage was $1100 which included a replacement valve components headset from a machine shop.
i have not heard of any car with a manage system which shuts motor down on overheating.
good luck

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