In Spain and other Mediterranean countries, some museums lack cooling and ventilation systems. They usually are located in historical buildings with heritage protection requirements. This is particularly complex in a building with a use that has to attend to comfort conditions for visitors and workers, and to very specific and demanding indoor thermal and relative humidity fluctuations for the conservation of its artwork collection. So, current requirements for museums and the hardening of summer conditions and the heatwaves events related to Climate Change require facing refurbishment measures usually related with the building envelope and the implementation of HVAC systems that require energy. This chapter presents a case study of a museum in the north of Spain, that has monitored data of 10 years (temperature and relative humidity), more detailed monitored data of 2019 summer with two very early heatwaves, and the analysis of different passive measures to implement attending to the characteristics of the building (with high thermal mass, without solar shading, and without ventilation and AC systems) in order to achieve suitable environmental conditions in a museum and with the lowest energy consumption, and “ready” for the hardening of summer conditions due to global warming.