## 1 Introduction  
In recent decades, the economy centred on the general reduction in energy consumption and CO\({}_{2}\) emissions has dictated important changes in every sector, especially in the construction world. Buildings are, in fact, key consumers of energy in Europe, and a rising tendency in energy use has been globally recorded in the last twenty years [1]. According to the European Environment Agency (EEA), in 2017 the transport sector accounted for 31% of the total final energy consumption in the European Member States, followed by households (27%), industry (25%) and services (15%) sectors [2]. The energy use in households is mainly related to space and water heating, which together are responsible for 80% of the total building energy consumption [3]. This high percentage is mostly due to poorly insulated envelopes and less-efficient heating equipment, which are mainly fossil-fuel-based and traditionally present in existing buildings. Similar trends are also estimated for greenhouse gas emissions. Buildings and construction together account for 39% of energy-related CO\({}_{2}\) emissions when upstream power generation is included [4]. Considering the high potential for cost-effective energy savings, the building sector has become a priority area for the European Commission, which has sponsored various actions to reduce the building requirement and promote their renovation. Prominent examples of this effort are the Directive 2002/91/EC [5] and the Directive2010/31/EU [6], commonly known as the EPBD (from its full name the Energy Performance of Buildings Directive) and its recasting. The first is mainly centred on defining a standardised methodology more oriented to new buildings. The second, on the other hand, aims to deal with existing buildings not only when they are subjected to a significant renovation but also in replacing and retrofitting a few elements or technical systems. After the EBPDs, the European Member States have shown a growing interest in building energy improvement, and, as a main result, a specific article centred on building renovation was introduced in the new Energy Efficiency Directive 2012/27/EU [7]. The great interest in the existing building stock is due to the fact that most European buildings currently in use were erected before the 1960s when the sustainability problem was in a preliminary phase, and energy building regulations were minimal. According to the Building Performance Institute Europe (BPIE) survey, in fact, 35-42% of these buildings date back to before the 1960s, and another consistent part was erected between 1961 and 1990 due to the massive boom in the construction sector [8]. The statistics underline the need for energy-efficient retrofit solutions, which are essential under present and, in particular, future conditions, considering that the construction age of a building is among the main features that affect its climate change vulnerability. Various innovations for improving the energy performance of buildings and, generally, cities, to reduce their environmental impact involve smart and intelligent devices, which are mostly renewable-based and installed directly on building surfaces [9; 10] or at an urban scale [11; 12; 13]. In this way, the present research aims to evaluate the climate change vulnerability of an existing building in Central Italy by estimating its energy needs and comfort rates under future meteorological conditions and considering both the current and energy-improved versions. In detail, the investigated retrofit solutions take into account the installation of Double-Skin Facades (DSFs) on the building's main elevations, and we analyse multiple configurations to assess the best typology for the specific climatic area. The novelty of the work lies, in particular, in locating the multi-layer facade on more than one elevation. Generally, in fact, DSF systems are placed on only one facade, the north one, and designed to act as a filter zone [14; 15; 16; 17; 18].