Climate change has physiological consequences on organisms, ecosystems and human societies, surpassing the pace of organismal adaptation. Hibernating mammals are particularly vulnerable as winter survival is determined by short-term physiological changes triggered by temperature. In these animals, winter temperatures cannot surpass a certain threshold, above which hibernators arouse from torpor, increasing several fold their energy needs when food is unavailable. Here, we parameterized a numerical model predicting energy consumption in heterothermic species and modelled winter survival at different climate change scenarios. As a model species, we used the arboreal marsupial monito del monte (genus Dromiciops), which is recognized as one of the few South American hibernators. We modelled four climate change scenarios (from optimistic to pessimistic) based on IPCC projections, predicting that northern and coastal populations (Dromiciops bozinovici) will decline because the minimum number of cold days needed to survive the winter will not be attained. These populations are also the most affected by habitat fragmentation and changes in land use. Conversely, Andean and other highland populations, in cooler environments, are predicted to persist and thrive. Given the widespread presence of hibernating mammals around the world, models based on simple physiological parameters, such as this one, are becoming essential for predicting species responses to warming in the short term.