Once you have it all apart, you may as well just service the cooling system altogether. Yes, it adds to the expense total, but I would consider not only changing the tstat and water pump, but also going to an aluminum t-stat housing, changing the hoses, the cooling fan clutch, and the water pump. If you don't know when the radiator and the overflow tank were replaced, do consider changing those too. It will be a pain to have to do this all over again in 9 months if you don't have to.
Also, use the BMW coolant. It was formulated especially to prevent electrolysis. Don't cheap out. Instead of getting it from the dealership, you can save some cash by buying from Pelican Parts or some other online store.
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