I didn't see any fault codes related to the thermostat. But I can definitely look again. That's a good idea - it hadn't occurred to me to check for that.

The coolant level sensor is installed in the expansion tank, but nothing is plugged into it. And I can't find a connector nearby. It should be right in the immediate area because there usually isn't any extra slack in the wiring. I'm going to unplug the sensor in my E39 528iT and see if it triggers the low coolant warning light. Then I'll know if that's causing a problem or not.