Thermal storage in aerated concrete: does it get warm in summer?

We have a meeting shortly with the first BU regarding the offer preparation. The question remains open whether Kalksandstein or Porenbeton should be used as the inner layer for the exterior wall:

The wall construction: 175 Kalksandstein or 175 Porenbeton || 160 Steinwolle 0,035 || 20 Luftschicht || 115 Klinker

The house will be located in a quiet residential area. For us, the question is whether the thermal insulation (0.154 W/m²K versus 0.2 W/m²K) or the heat storage capacity is more important.
Does anyone have experience with such a construction using Porenbeton? Does it always get warm in summer?
The interior walls will be 115 Kalksandstein or in some places 175 Kalksandstein.

Thanks for your opinions.

Facing the same question, no one has an idea?

The question is also, what kind of brick (color)? A dark stone can quickly become 30 degrees or more warmer than a light one, and the heat naturally also penetrates further inside...

For us personally, the walls are not even the problem but the windows heat the place up significantly in summer, plus the dark floor on which the sun beats, etc... I would have rather invested money in roller shutters or a geothermal air exchanger for the controlled residential ventilation