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The preservation of historical buildings, as well as museum exhibition facilities, is critical under the changing environmental conditions. Since the potential outdoor climate changes may affect the recommended environmental conditions within the museum microenvironment, there is an urgent need for further research into the relationship between the outdoor and indoor climate and how future changes could affect it. This study investigated the relationship between the indoor and outdoor climate conditions in museums and historical buildings located in Greece. The main goal of this work was to assess the suitability of the indoor microclimate by applying the heritage microclimate risk (HMR) and the predicted risk of damage (PRD) indices. In order to achieve a detailed assessment of the present temperature and relative humidity (RH) outdoor conditions over the specific case studies, data from three different sources were incorporated in the study (observed, reanalysis, and model data). The model data were derived from the regional climate model RegCM4 with a fine spatial resolution of 10 x 10 km. The indoor environmental parameters were collected both from the museums and the historical buildings in the two case studies. In cases where indoor environmental data were not available, monitoring sensors were installed. The findings indicate that in cases where there is no control over climate conditions, the indoor climate is predominantly influenced by the outdoor climate. As a result, these spaces exhibit a heightened sensitivity to potential future temperature increases. [ABSTRACT FROM AUTHOR]