The indoor climate conditions being suitable for the conservation of cultural heritage can be conflicting with energy saving and thermal comfort. Moreover, the moisture dynamics have not been studied enough in the simulation of the indoor environment, even though its interaction with artworks is crucial in deterioration phenomena. This research aims at defining a strategy, based on experimental data and dynamic simulation of hygrothermal behaviour, in order to design a HVAC system able to simultaneously satisfy conservation, thermal comfort and energy requirements. A weighted function for the multi-objective optimization has been proposed and effectively used to pinpoint the combination of temperature and relative humidity set-points.