In temperate climates, such as most Italian ones, the need to limit both winter heat losses of buildings and their overheating in other periods is present. Moreover, in warmer Mediterranean climates the convenience of insulation against the thermal inertia of the building must also be evaluated. Therefore, when the energy renovation of an old building with heavy masonry is performed it is a question of optimizing the position and the thickness of the additional insulation. In the presence of extended glazed surfaces, another problem is the choice of the solar control strategy. Both problems are present in many old Italian public buildings. In this paper is presented a computerized methodology for optimizing these choices taking into account the interactions between mass, additional insulation, internal and solar gains. The case study consists in a typical school building from the early 1900s. The thermal behaviour of the building was simulated in different Italian climates: Bologna, Roma and Palermo. The effects on energy demand and comfort of various solutions were compared. The possible effects of different types of masonry, different building’s orientations and various intended uses were also explored. Simulation results provide some indications as function of climate and building’s intended use. They show that the ideal strategy of intervention, for the type of building considered, depended not only on the climate but also on the building’s intended use, which determined the internal gains and the time profile of use.