Air-to-water heat pump - Nest Thermostat

You are under the misconception that this costs you a lot of energy – due to the self-regulating effect, it is actually cheaper than isolating the room and thereby including the other rooms.

In general, there is the law of conservation of energy, which you hopefully do not want to doubt. As long as I do not ventilate energy to the outside, energy can only leave through exterior walls, windows, roof, and floor slab. In this case, an exterior wall with a temperature difference between inside and outside that is 4° lower should release less energy to the outside than a fully heated room. So the house should overall require slightly less energy. It is logical to me that these are not exorbitant amounts. However, you claim that due to the self-regulating effect of the underfloor heating, more energy is consumed. Since energy cannot be lost according to the law of conservation of energy, it must leave the house. At which point exactly?

No, through the self-regulation effect you save - you destroy it with the ERR.

That makes total sense to me! So why are ERR still being installed in air-to-water heat pumps with underfloor heating? The system is completely obsolete.

Because it is factually predetermined and sells well (the technology is quite cheap, but you quickly pay four figures for an entire house).

Is it just about the money? When I look at the recommended system controller from Vaillant...450€ each

The system controller from Vaillant is included with my heat pump - and should not be confused with a thermostat for an ERR. You misunderstood something or the hotline told you nonsense - you can use it as a remote control - but you can also leave it plugged into the heater. I didn’t think it was unattractive and it will be installed in the living room.