In civil engineering and architecture, sustainability requires energy optimization minimizing the energy amounts needed for heating and cooling. Revitalization of built heritage, except the renewal of the original identity, and preservation through adaptive reuse, must meet the requirements set within the framework of energy postulates. Given that the physical interventions for improvement of energy efficiency can affect the visual appearance of the building, energy retrofitting of built heritage under the protection regime represents a challenge in the management of cultural heritage. The paper aims to identify the most optimal measures to be applied to increase energy efficiency, depending on the protection level, using the fuzzy Analytic Hierarchy Process (AHP) method. Results show that for the highest protection level, the maximum degree of optimism indicates complete preservation of building identity, favoring indicators related to the technical systems, while for the medium protection level, all degrees of optimism favor internal insulation of thermal barriers and collector walls. Despite the allowed interventions for the lowest protection level, the optimistic view suggests alternative solutions not to greatly undermined identity. At the maximum degree of optimism, the application of indicators for technical systems dominates, which only in the last resort makes changes to the building.