## 1 Introduction  
Traditionally, comfort and conservation in museums impose the use of tight ranges of temperature and relative humidity [1; 2; 3; 4; 5; 6], sometimes with no scientific justification. Take the case of the National Museum of Ancient Art of Lisbon (NMAA), which imposes a tight climate control of 20-22 \({}^{\circ}\)C and 50-60% RH even though the building is unable to comply with it for percentage of time that can be considered satisfactory, as concluded by the authors in [2]. These constraints, coupled with the poor hygrothermal response of ancient buildings, lead to high energy consumption. Rising environmental concerns and the publication of directives in the pursuit of greater sustainability and reduction of global warming that emerged over the last two decades have led to hygrothermal rehabilitation of buildings which significantly contribute to the total energy consumption in Europe [7]. The European energy policy has become more demanding and the European Union (EU) has taken energy efficiency as an urgent need, developing some ambitious directives aiming to achieve energy reduction in the building sector, where it is possible to highlight the 2018/844/CE [8]. This directive is very demanding and binding on new buildings or extensive rehabilitations, but leaves cultural heritage buildings out given their needs and specificities, namely the risk of loss of identity and historical quality induced by invasive interventions [6; 9]. However, this new version specifies the following need:\"Research into, and the testing of, new solutions for improving the energy performance of historical buildings and sites should be encouraged, while also safeguarding and preserving cultural heritage\"_ [8]  
Despite these directives, the evolution of energy consumption in the services sector, including museums, does not follow the global trend of energy reduction, as can be seen in Figure 1. It is possible to see a sharp decrease during the period of the public debt crisis in the Eurozone and during the pandemic, but the global trend since 2000 is of an increase in the final energy consumption. Comparing the period before the pandemic--up to 2019--and taking the year 2000 as the reference, the EU27 presents an increase of around 23% and Portugal an increase of 68% [10]. The ineffectiveness of European policies to reduce energy consumption in the services sector in general, and in particular in cultural heritage, cannot be solved by the publication of new directives focusing solely on energy, since the patrimonial character associated with these buildings does not allow it, thus enhancing the need to find a balance between conservation, comfort and energy [11] rather than an incessant search for the numbers. Despite all the evolution in the use of passive techniques in the design of new buildings and in rehabilitation, the intervention in classified buildings is not obvious and is impossible to standardize [9; 12; 13]. Due to the impossibility of changing the original architecture [14; 15], quite often a change in the climate control strategy, window refurbishment or, in some cases, the use of thermal insulation in the interior are some of the most obvious solutions to implement. Furthermore, it is necessary to take into account the impact of climate change when making decisions about the interventions that will occur [16]. An extensive literature review on the use of thermal insulation and windows in historic buildings can be seen in [17]. The impact of thermal rehabilitation and climate control strategies on cultural heritage has been studied by several authors [7; 18; 19; 20; 21; 22; 23]. Interesting results were obtained by [PERSON] et al. [7], for example, achieving energy savings of around 77% for a Dutch museum by changing the original constant set-point of 21 \({}^{\circ}\)C and 48% RH to a less demanding target--40-50% RH--and a dynamic temperature set-point based on an adaptative thermal comfort model and in free-floating at the night time.