Energy rehabilitation of heritage buildings used as museums presents unique challenges, as it must balance the preservation of cultural heritage with achieving comfortable indoor conditions for visitors and staff. These objectives often conflict, requiring innovative approaches. We propose a methodology that uses dynamical simulation with EnergyPlus and multi-objective optimization with jEPlus + EA software to reduce energy consumption and maximize comfort while maintaining architectural integrity and conservation conditions evaluated by a quantitative analysis based on the European Standards. The framework also includes monitoring microclimate conditions and assessing the risk levels of the exposed collections. A case study in Salta City, Argentina—a historical building repurposed as a museum—illustrates this approach. Results show improved energy performance and comfort conditions for visitors, with an annual energy requirement of about 36% of the original requirement (16.4 kWh/m2 versus 45 kWh/m2) and a decrease of about 32% in the discomfort hours (from 5362 h to 3643 h). Additionally, conservation conditions improved, achieving a more stable microclimate for air temperature and relative humidity. The framework proved useful for evaluating retrofit solutions that enhance the building’s energy performance and comfort without compromising the conservation conditions of the exhibited collections.