The renovation of buildings impacts various factors; one of them is the economic aspect, which has a significant influence on the decision-making process in building refurbishment, especially in social housing. An often-neglected aspect of renovation is the influence of climate change. Typically, historical climate data are used to estimate the building’s future energy needs. However, due to climate change, this approach may fail to accurately represent future environmental conditions, resulting in miscalculations in energy consumption and costs. This study analyzed a building archetype obtained from the TABULA webtool with the characteristics of a social house building located in Trieste. Dynamic simulations were performed using DesignBuilder and EnergyPlus software and future climate models (the GERICS_CNRM-CM5 and GERICS_IPSL-CM5A-MR models obtained from the EURO-CORDEX database). The projected energy needs of the renovated building and its economic effects were compared with current scenarios, and due to the uncertainties in economic parameters, the outcome is expressed in terms of percentiles of the Net Present Value (NPV). The results of this study show that since temperature increases in the future, the need for energy in the heating period reduces, while the need for cooling increases, directly affecting the statistical distribution of the NPV.