## 1 Introduction  
To regulate temperature and humidity in buildings, it is not always possible to alter the building envelope or to install air conditioning systems, especially in historic buildings, such as churches. Consequently, indoor surfaces and hygroscopic building materials are subjected to daily and seasonal temperature and Relative Humidity (RH) fluctuations, which might degrade buildings [1, 2]. For these reasons, it is important to understand the impact of temperature and humidity on buildings, as well as the response of materials to climate variations [3, 4].  
Indoor climate in buildings without any conditioning system is mainly determined by the outdoor climate and hygothermal performance of the building enclosure [5]. The lack of heating and well insulated walls might generate significant daily or seasonal indoor humidity and temperature fluctuations, depending on the climate and location of the building [6; 7]. The simultaneous variations of temperature and RH can produce significant variation in moisture exchange between materials and the environment [8].  
Moisture transport and storage capacity of interior surface materials due to varying humidity in the indoor air is of importance both for the humidity levels of the room itself and for the moisture impact on walls surface materials [9]. There is research [10; 11; 12; 13], standards [14] and some ongoing measurements on this topic [15] that pointed out the importance to understand the impact of moisture to materials durability, indoor thermal comfort and health. [16] took a step further, by considering periodic humidity variations and by applying moisture buffering experimental results into simulations. However, the focus of most of the studies was mainly on the sole RH variations, while temperature was always considered non-variable. The observation of daily indoor climate variations in non-conditioned buildings suggested a simultaneous opposite and quasi-sinusoidal temperature and RH fluctuations [6; 7; 17]. Some recent results on this area [1; 18] gave new analytical expressions for the effect of combined variations of RH and temperature. [PERSON] et al. [18] analysed experimentally the moisture uptake of wood and introduced a calculation model that took into account simultaneous temperature variations together with the surface resistance of the material. However, the model was based on a specific material and required an elevated number of material properties and experimental analysis.  
In a newly published study [19], a detailed analytical solution for temperature and RH square shaped variations was proposed. The method was developed by neglecting the surface vapour resistance and by considering a semi-infinite material [20]. The objective of this study was to further develop the analytical model from [19], by introducing triangular and sinusoidal temperature and RH variations. To validate the analytical method, results were compared with laboratory experimental tests on clay and gypsum plasters. The materials mass variations to simultaneous temperature and RH variations was observed and compared with simulations. The aim of this paper is to introduce new experimental approach to evaluate the moisture buffering capacity of materials and use experimental data to realistically simulate the materials behaviour. The effect of the surface resistance was implemented in the model and the validity of the semi-infinite approach on the moisture uptake was analysed. By improving the model and approximating the indoor daily variations to sinusoidal and triangular, it was possible to develop a reliable simulation method that is able to predict the materials response in a non-conditioned environment.