I am really impressed by what has accomplished here - WOW!
As an amateur, when I read the thread title, namely that rooms quickly become very warm or overheated in the sun, in my opinion it is primarily because a sluggish underfloor heating system is usually used. This system has many advantages and is probably considered standard at the moment, but THAT also seems to me to be a noticeable disadvantage alongside the many benefits.
Currently, we have an underfloor heating system that was probably installed in a rough-and-ready manner (it doesn’t belong to us). Today, for example, the sun is shining a bit and although we have hardly any direct sunlight despite many windows, it is noticeably warm, and without open doors and windows it would be uncomfortably warm for me, whereas otherwise it is well tempered here.
In the old house we had the classic radiator heating, and I generally prefer it a bit cooler and then heat up as needed (central heating or wood stove) or turn it back down again.
The problem mentioned here should therefore also occur with a gas heating system, and the cause is probably to be found in the underfloor heating rather than in a heat pump or gas heating system.
Or am I mistaken?
Unfortunately, the heating topic has not yet been discussed in detail with us, but especially because of the inertia of the underfloor heating, I am indeed considering installing a classic (disdained) radiator heating system, even if I would lose wall space for the radiators. We’ll see.....