The effects of changes in Global climate on the prolonging time and the frequency of the periods of very high outside air temperature at summer were shown in the paper with particular emphasis on European moderate climate countries. In these countries, residential buildings, are usually equipped neither in air conditioning equipment, nor in ordinary window blinds. As the most promising solution it is suggested to resign completely or partially from ground slab thermal insulation, directly utilizing ground heat storage capacity. The paper includes detailed simulations on potential effect of various kind of floor construction and actions preventing high indoor air temperatures in building approach on air temperature inside the one-storey, passive residential buildings during consecutive days of very high outdoor temperature and total energy used yearly for additional heating and air conditioning.