Predicting species range shifts in response to environmental change requires the determination of regions where individuals maintain a positive energy budget. For hibernating animals, this budget depends on two physiological states (normothermy and torpor) that alternate in response to ambient temperature. To study range shifts of hibernators like the common noctule (Nyctalus noctula), we developed an ecophysiological approach that integrates metabolic rates, physiological states, and environmental conditions. Our model accurately hindcasted the northward range shift of this migratory bat over the past 50 years. Under climate change forecasts SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, for which winters will shorten by 1.4-41 days and warm by 0.11°C-2.3°C, the hibernation area is predicted to shift by 78-732 km and expand north-eastward by 5.8%-14% by 2100. Mean ambient temperature and winter duration prove sufficient to approximate the hibernation niche and may be used to predict changes in hibernation areas where collecting physiological measurements is difficult.