Example: Suppose I have a house made of natural stone. We are now talking about one wall of it. It has no window and nothing!
This natural stone construction "insulates" the house according to the Energy Saving Ordinance, without additional insulation.
This wall is then warm/red in the evening and cold/blue during the day.
From a certain thickness: No!
You are making wrong basic assumptions. The natural stone wall only needs to be thick enough, then there is nothing red in the evening that was still blue in the morning.
Physically, this is due to the heat capacity. In winter, your warm indoor air has to warm up the wall. Compared to the wall, air has a very low heat capacity (calculated per volume). The wall has to absorb a multiple(!) of the energy that all the indoor air in the house has in order to even "reach temperature" (because of the high heat capacity).
This means that you can only achieve a temperature difference between the outside of the wall and the interior in winter with a long heating period and a high temperature difference between outside and inside. So no warm/red evenings.
The principle works in summer, when it is warmer outside than inside and vice versa, such a house stays cool for a long time. In winter, however, you also have colder walls inside than with other wall structures.
Such a masonry "consumes" energy, simply because it can absorb an enormous amount of it due to its high mass without immediately showing large temperature effects. Classic insulation materials are comparatively light (less mass) and simply have poor thermal conductivity, which is why they can achieve the same effect without absorbing much energy (and thus valuable heat).