I just recently experienced the same problems as yourself.
My heater core was the cuplrit, as that is where I was losing coolant, but this does not sound like your problem.
The problem with your temperature rising and falling has to be 1 of 2 things, a bad thermostat, or an improperly bled cooling system. Is your overfill tank filled with coolant? If not keep adding coolant after the car cools down until it remains full even after the car cools down, I understand this is how you bleed the cooling system.
Your waterpump sounds OK, if the propellars are in tact, but maybe it is not spinning adequately.
I would focus on ensuring your system is bled properly, as I think that may be the culprit. Remember to run your heater on full blast to fill the heater core with coolant.
let me know what you find out.
1994 325iC, 130k miles
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