@feld My Netatmo doesn't do all that, and neither do the other thermostats connected to the other boilers I have access to.
Fundamentally, those are things the boiler handles (if it's less than 20 years old), not the thermostat. My boiler, even though it's 10 years old, has all these internal features; it also controls the water temperature, etc.
The thermostat is just for deciding if the house is cold or not - I expect all the other controls to be handled by the burner itself.
In other words, I'm not replacing the internal thermostat (the one that regulates the flow temperature, etc.), just the room thermostat. Besides, my sensor is located very far from the boiler, which is in a separate, ventilated room.