There's also one other component...BMW added it to e30's to prevent the heater core from popping under high pressure. It's a small bypass located in the input hose from the head to the core. The bypass connects to the output hose, thus preventing hot coolant from over-pressurizing the heater core.
I'm not sure if it's a pressure regulator, thermostat or both. If it's bad, the heater core won't work but the car will otherwise function normally.
Did you run a pressure check on the system? The caps do eventually fail, and IIRC they run at 2 bar, quite a bit higher than the more common 15psi caps on many other cars. If that cap isn't maintaining specified pressure, the car will overheat.
Also be extremely careful when bleeding the radiator...that little plastic bleeder will snap in two if you look at it the wrong way. I carry a few spares in my trunk toolkit, just in case.