Over heating recently in new to me 97 Z3 2.8

[Wheatchex1]

Recently I purchased a 97 Z3. It's got 64k miles and according to the previous owner he had it for 7 years and drove it 200 miles per year so probably no maintenance. I have put about 2k on it since purchase at end of August. Ran fine with minimal issues. Only issue was with not much cabin heat intially unless high rpms or on highway. I assumed this was odd but normal since this is my first BMW and I eventually had heat. Fast forward a month and wife and I went to breakfast and car wouldn't have cabin heat even though yemp gauge was in middle. Then gauge started to head into red zone. Fortunately we were where were going and had breakfast and let it cool down. Started it up and drove home, started to heat up about 5 mins from home and again to red zone. Parked since. Some signs of coolant escaping from coolant tank. I've got a new water pump, thermostat and thermostat housing(aluminum) to be installed. This is based on reading that water pumps need to be replaced between 50k and 60k miles. Is there anything else I am missing? Thank you for any insight you all can provide.

[bluptgm3]

Look for porosity in the cast surfaces of the alloy T-Stat housing. I have had good luck with Ronak.
Many will recommend the BMW plastic T-Stat housing.


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[Vintage42]

Recently I purchased a 97 Z3. It's got 64k miles ... not much cabin heat intially unless high rpms... gauge started to head into red zone... started to heat up about 5 mins from home and again to red zone. ... coolant escaping from coolant tank...

You lost coolant to the head and the heater core. If you did not drive in the red zone, perhaps the engine can be saved. Do not drive again until the cooling system is completely replaced.
You have not told the kind of engine or the miles, but it does not really matter after your event.

[me77]

If you're lucky, the missing cabin heat at idle was just a sign of an improperly bled cooling system. Not ideal, but better than no coolant at all flowing through the system. If coolant came out of the expansion tank that means that either your cap is faulty or that the pressure in the system went above 2.0 bar (29 psi).

[Vintage42]

I am not sure which is higher in elevation, the head or the heater core. Hopefully, the heater core loses coolant first and won't make hot air. But that would not make the gauge rise. If the gauge rises, it must mean the head has lost coolant.

[deni2s]

No cabin heat at low rpms is sign of low coolant and air bubble in the system.
2.8 is pretty strong engine, might easily be fine after temp in red zone for short time.
I would start by finding the cause of issue(s), before starting to replace any parts.
Start with checking engine oil level (shouldn't be too low, shouldn't be too high), filling the coolant and bleeding the system properly - heater has to blow hot at idle. Check for leaks in cooling system. Check that there is a flow in expansion tank. Monitor the coolant level regularly (only when cold).
Make sure you don't have smaller radiator from 4 cylinder z3 (I had seen a couple "fixed" cars this way.)
Make sure clutch fan is engaging properly. Replacing it together with new fan blades might be not a bad idea.
Make sure temp switch (in radiator) connector has brown wire in the middle - some cars were wired incorrectly from factory.
Replacing thermostat is not a bad idea. Try to test old and new one in boiling water while measuring temp at which it opens and closes to be sure.
Heater valve theoretically might be a suspect, but I don't think so. Last time I suspected heater valve after replacing cooling system, better bleeding at 3000 rpms while pushing all hoses for 10 minutes finally pushed the air out of the heater and got the hot coolant in.

It's possible, that you bought already overheated engine, which means it could have leaking head gasket or cracked head. Driving 200 miles per year that issue might not even be noticeable. Check that you don't have excessive sweet white smoke out of exhaust. Check that sweet tasting water is not dripping out of exhaust (some water out of exhaust while cold is fine).