In the urban context, buildings play a key role as they are energy consumers. In well-established cities with a high percentage of aged building stock, the focus should lie on sensitive urban areas where the weakest population sectors and the worst economic conditions are usually encountered. In this work, the energy refurbishment of social housing is proposed. A block of municipally owned buildings is selected as a case study to consider that public buildings play an exemplary role according to Directive 2012/27/EU. The group is formed by 12 buildings, which account for 120 dwellings. This study is grounded on two levels. First the urban level. The building is located in a prioritized urban Area of Rehabilitation, Renovation and Urban Regeneration (ARRU), according to the new local Land Plan. This area presents multidimensional vulnerability and considers urban, building, socio-demographic and socio-economic features. Second, the building presents very low energy performance. It was built in 1959 when a high demand of dwellings and the economic resources then available led to low-quality buildings that are far from meeting today’s standards.