The ventilation system shovels the warm air into the house. In addition, the masonry heats up. Since everything is well insulated, the heat is retained very well inside. The air exchange rates of a normally designed ventilation system are not suitable for cooling. The only solution here is to turn off the ventilation during the day and cool with a split unit. Alternatively, install a very large ventilation system (with sufficient supply and exhaust air valves), a refrigeration unit, a cooling buffer, and a chilled water coil. If the unit is reversible, it can also be used for heating. However, this is uncommon in single-family houses.