The e-SAFE innovation project financed by the Horizon 2020 Programme and led by the University of Catania, is developing, testing and demonstrating an innovative combined energy-and-seismic renovation solution for Reinforced Concrete (RC) framed buildings based on the addition of Cross Laminated Timber (CLT) boards to the outer walls, in combination with wood-based insulation. In this paper, the proposed renovation solution (called e-CLT) is investigated in terms of moisture-related risks, i.e., the mold growth and the increase in heat losses due to Liquid Water Content (LWC) within building materials. To this aim, dynamic simulations are performed by means of Delphin 6.1, thus including combined heat and mass transfer (HAMT) due to water vapor migration and accumulation. The results show that, although there is no significant risk of mold growth in the e-CLT for climate conditions prevalent in Northern Italy, the moisture content within the materials implies an increase by about 10 % in the heat losses if compared with a dry wall. Furthermore, inaccurate material properties and boundary outdoor climate conditions can affect the reliability of the results: for this reason, a more appropriate hygrothermal characterization of materials is recommended, as well as the identification of suitable climate datasets, which, however, are not always available.