And fate strikes again: During routine maintenance, the shop noticed the car running hot, and a slight film of oil in the coolant.
Sniff test concluded no CO2 leak, so while the oil has come from somewhere, that alone shouldn't be sufficient for the temperature increase.
First swap was done on the thermostat, but that didn't cure it.
Now they'll swap the water pump (hooray), and we'll hope that that fixes it - but the waterpump was just replaced two years ago, and the error mode is certainly not common.
Since higher revs make for worse cooling performance, it is the most likely cause though, so I hope this premature belt and pump service is going to get the car back in my hands, before the autumn season kicks off. At least July saw no driveable days, so so far the loss wasn't immense.