From this thread - sorry, not good news, your symptoms seem to match exactly:
txusa03: I replaced the pump, thermostat, and the 3 Aluminium bolts that secure the pump to the engine block, plus coolant naturally. The new thermostat is made of plastic rather than Aluminium - so I guess that is the mysterious 3rd part you mention.
tuned2ride: Symptom was amber overheating warning, closely followed by red overheating alarm. I quickly pulled over and stopped engine. Upon checking under bonnet, radiator + hoses were cold, but small amount of coolant had vented.
I checked interior heating, and that was cold too. Luckily I was only a mile or so from home so waited for about 10 mins with engine off and drove gently for a minute then stopped for 5 - etc till I got home. I wouldn't necessarily recommend doing this - especially in warmer weather / climate. But in my case I luckily never got another warning on my limp home, and no more coolant was vented.
If a significant amount of coolant was allowed to be vented then one could risk causing engine damage.
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I got the red overheating alarm a couple of days and took it to the dealership. They said that I had to replace: Water pump + thermostat + VANOS solenoid.
Currently have ~130,000 miles on the car, so I was out of warranty.