In museums, hygrothermal conditions must be carefully controlled by HVAC system to avoid artwork degradation. Higher energy requirements are needed for the maintenance of the suitable thermal environment. Moreover, a comfortable thermal sensation is needed for a positive museum experience. In light of current policies on energy efficiency, we propose an original procedure for the concurrent achievement of three goals: artwork preservation, energy efficiency, and human thermal comfort. This procedure is based on the application of multi-objective optimization and aims at correctly choosing temperature and relative humidity setpoints, through the use of dynamic simulations and evaluation of three indexes as objectives. This strategy can be particularly effective in museums hosted in historic buildings, where envelope and HVAC refurbishment is often forbidden or discouraged due to the architectural constraints. Furthermore, the retrofit action is almost costless. A case study is presented: first, a monitoring campaign in an Italian museum has been used for the validation of dynamic simulation models of the building-HVAC system; then, the validated models have been used to show that improvements of artwork lifetime, human thermal comfort and reduction of energy requirements of the HVAC system are possible, if currently-used hygrothermal setpoints (based on technical standards and guidelines) are replaced with those identified by the optimization problem.