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The aim of Sustainable Development Goal 7 is to ensure access to affordable, reliable, sustainable and modern energy for all. Increased energy efficiency is particularly important in the construction industry because urban agglomerations currently consume up to 80% of global energy, 40% of which is attributable to buildings. In countries like Italy however, where historical buildings constitute a significant part of the building patrimony, improving energy efficiency is not always straightforward as interventions must take into account the historical materials used as well as the context of the construction. Therefore, the aim of this research was to establish a methodology that would identify the most effective means of achieving energy efficiency taking into account the historical aspects of a building and its cultural context. The methodology proposed and described in this paper involves: preliminary analyses to identify the elements of value and the level of transformability of facades; the selection of different insulating materials; dynamic simulations of building behaviour; analyses of intervention costs in relation to each type of insulation and finally the preparation of a multi-criteria matrix to identify the most effective method of improving energy efficiency of a historical wall with differing degrees of transformability. Each insulating material was analysed in relation to heating and cooling requirements and material cost impact. The methodology was applied to a case study in the Province of L'Aquila, Italy. In the paper a multicriteria framework, for the improvements in the thermal efficiency of a building, it is presented. Specifically the attention is focused on heating requirements, cooling requirements and cost impact. The results indicate that, with respect to historical building, it is possible to adopt strategies finalyzed to improve the energy efficiency of these buidings, contributing in this way, also toward the SDG7. Specifically, the best performance for a wall with a high level of transformability can be obtained using calcium silicate, extruded polystyrene, kenaf and hemp, whilst, in the case of a wall with a low level of transformability, the best materials are calcium silicate, polyurethane and linen fiber. Finally, in the case in which external constraints prevent the application of a thick coat and internally there is limited space, the use of calcium silicate was found to be the best energy efficient measure. [ABSTRACT FROM AUTHOR]