Increases in the frequency and intensity of heat waves are direct consequences of global climate change with a higher risk for urban populations due to the urban heat island effect. Reducing urban overheating is a priority, as is identifying the most vulnerable people to establish targeted and coordinated public health policies. There are many ways of understanding the concept of vulnerability and multiple definitions and applications exist in the literature. To date, however, nothing has been done on the territory of this study, the metropolis of Lyon (France). The objective is thus to construct two vulnerability indices: physiological, focusing on the organism's capacities to respond to heat waves; and socio-economic, based on the social and economic characteristics and capacities of the community. To this end, two complementary methodologies have been implemented: the AHP (Analytic Hierarchy Process) and the PCA (Principal Component Analysis) with Varimax rotation, respectively. The results were then spatialized to the smallest demographic census unit in France. The areas highlighted differed due to conceptual and methodological differences: the highest physiological vulnerabilities are in the center while the socio-economic ones are in the eastern periphery of the urban area. The location of these areas will enable prevention campaigns to be carried out, targeted according to the publics concerned.