I have my doubts whether this will cool down so quickly. The wage-price spiral is just beginning and interest rates are still comparatively low. Accordingly, quite a few will still want to convert their available cash into real estate. Interest rates are one factor, but another is the expectation for the future. As long as enough buyers assume prices will rise, they will continue to rise.
At this point, I would also slowly start to differentiate between new construction and existing buildings. In new construction, you have a modern house from the outset with good insulation, a heat pump, and photovoltaics. In most older buildings, on the other hand, an expensive core renovation is necessary if you want to properly meet future regulations. Simply replacing the oil burner with gas is no longer an option. With CO2 pricing as well, a lot will still come upon those who operate their old buildings with an existing gas heating system.