A thermodynamic analysis of population dynamics and of sustainability provides rigor to many important issues. In this work, the “system Society” is analysed in connection with the “system Environment” using an exergy metric, and the method includes an internalization of the Externalities (Capital, Labour, Environmental effects) conducted on the basis of a “system+ environment” balance. In this perspective, this study investigates the Late Pleistocene extinction of the Homo Neandertalensis, which took place in a geologically short time and in the presence of a competing species, the Homo Sapiens. The case in study is not trivial, and its choice not casual: in those times, the only factor that could lead to an advantage of one group over the other was their respective resource use intensity. A specific indicator, the Exergy Footprint, is here applied to measure the total amount of primary resources required to produce a certain (material or immaterial) commodity, including the resources needed for the physical survival of the individuals. On the basis of the available data, the results show that the EF of the Neandertal was higher than that of the Sapiens, and that, both species sharing the same ecological niche in a time of dwindling resources, the less frugal was also more fragile in an evolutionary sense.