## 4 Discussion  
The present experimental study aims to investigate the thermal behavior of a high thermal inertia building, characterized by two different external insulating materials, under Mediterranean climatic conditions. The monitored mockup is made of a lightweight concrete (LWC) with lightweight recycled glass aggregates; its walls, floor, and roof have a thickness of 70 cm to guarantee high thermal inertia. Thus, the initial building (W0) is a massive structure with high thermal capacity (840 kJ m\({}^{-2}\) K\({}^{-1}\)). In order to reach the National standard for thermal transmittance (U), two different external insulating layers are added on the Southeast facade, i.e., thermal plaster and XPS, named W1 and W2, respectively, which have similar thermal conductivity, but different specific weight \(\rho\) and water vapor permeability \(\mu\). Data recorded during the two monitoring campaigns in 2018 and 2019 confirm the repeatability of the different observed behaviors of the two insulating systems. Figure 16: Comparison between recorded and simulated values of W1 and W2 on 10 –15 July. Figure 17: Comparison between recorded and simulated values of W1 and W2 on 2-7 August. Collected data demonstrate a relationship between monitored external surface temperatures on insulated walls W1 and W2 and weather conditions, namely air temperature and solar irradiance. Results show that W2 undergoes higher thermal stress than W1, due to higher peaks in external surface temperature and large fluctuations in daily temperature. This behavior is highlighted through statistical data, such as standard deviation calculated for the external surface temperature, as reported in Tables 5 and 6. The W2 values are 19.1% and 18.0% higher than W1 in July and June 2018, respectively. Analyzed results show that the XPS insulated system (W2) heats up more and faster than the thermal plaster insulation (W1) but releases the stored heat more quickly. A deep analysis of the properties of the two external insulating systems could explain this behavior. First, the thermal resistance of W2 (2.22 Kmq/W) is twice that of W1 (1.08 Kmq/W), due to similar thermal conductivity but W2 is twice as thick as W1. Therefore, a more performing external insulation limits the transmission of the thermal flux toward inner layers of the wall, thus, the superficial external surface shows an increase in temperature. Secondly, the external areal heat capacities of the two walls could be considered: 15.6 and 9.3 kJ/m\({}^{2}\)K for W1 and W2, respectively. This parameter assumes high relevance for a proper building envelope design in accordance with the research of [PERSON] et al. [23], in which the internal areal heat capacity is analyzed to prevent indoor air overheating. Moreover, it is significant to observe that both internal surface temperatures result almost linear and do not undergo considerable fluctuations, due to the high heat capacity of the massive building. Therefore, indoor air temperature does not significantly change and even equal internal surface temperatures of W1 and W2 in the warmest period of August. Contrary to the external surface, monitored surface temperatures between the insulating layer and LWC show a different behavior; indeed, W1 displays larger fluctuations. The reason should be found in thermal conductivity and thickness of the different insulating layer, as previously stated. In order to guarantee indoor thermal comfort, proper design of the building envelope is of utmost relevance in Mediterranean climates characterized by warm summer. This experimental study highlights the importance of thermal inertia in building envelope, focusing on parameters such as external areal heat capacity (k\({}_{2}\)) and thermal resistance (R). Specifically, a high value of thermal resistance of the external insulation and low value of external areal heat capacity (k\({}_{2}\)) on a massive building causes external surface overheating problems, thus, not representing the best construction solution.