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This study aims to assess the impacts of climate change on the cultural heritage of two Greek areas for both the present time and the future. As the climate is constantly evolving, cultural heritage is continuously exposed to the risk of damage and deterioration. Therefore, museum directors and boards as well as the national ministries must be informed so that measures and practices are adapted to the new climatic conditions. Greece is a country with immense cultural wealth, both tangible and intangible, which stretches back four and a half thousand years. As a homeland of important historical and cultural resources, Greece is vulnerable to climate change. Two up-to-date indices were applied to two Greek areas with high cultural value: Thessaloniki and Delphi. In order to evaluate the suitability of the microclimate and to assess the damage risk, the Heritage Microclimate Risk (HMR) index and the Predicted Risk of Damage (PRD) index were used for two variables: temperature and relative humidity. The study was carried out for three different time periods, the period 1980–2000 (hereafter, the reference period) and the future periods 2039–2059 and 2079–2099. For the reference period, data from three different sources were incorporated in the study (observed, reanalysis, and model data). The simulated data were derived from the Regional Climate Model RegCM4 with a fine spatial resolution of 10 × 10 km. In addition, the emission scenario RCP4.5 was used for the model’s future simulations. The present and future ideal outdoor climate conditions for the monuments were also estimated and are presented in this work. Overall, the future estimations revealed that the ideal outdoor temperature conditions will be higher compared to the reference period, meaning that the monuments will have to adapt to new warmer climate conditions. In addition to the new temperature conditions to which the monuments will have to adapt, the study showed that the monuments will be exposed to “moderate-maximum” risk more often in the future.