The global average air temperature is increasing as a manifestation of climate change and more intense and frequent heatwaves are expected to be associated with this rise worldwide, including northern Europe. Summertime indoor conditions in residential buildings and the health of occupants are influenced by climate change, particularly if no mechanical cooling is used. The energy use of buildings contributes to climate change through greenhouse gas emissions. It is, therefore, necessary to analyze the effects of climate change on the overheating risk and energy demand of residential buildings and to assess the efficiency of various measures to alleviate the overheating. In this study, simulations of dynamic energy and indoor conditions in a new and an old apartment building are performed using two climate scenarios for southern Finland, one for average and the other for extreme weather conditions in 2050. The evaluated measures against overheating included orientations, blinds, site shading, window properties, openable windows, the split cooling unit, and the ventilation cooling and ventilation boost. In both buildings, the overheating risk is high in the current and projected future average climate and, in particular, during exceptionally hot summers. The indoor conditions are occasionally even injurious for the health of occupants. The openable windows and ventilation cooling with ventilation boost were effective in improving the indoor conditions, during both current and future average and extreme weather conditions. However, the split cooling unit installed in the living room was the only studied solution able to completely prevent overheating in all the spaces with a fairly small amount of extra energy usage.