Conservation of species under climate change relies on accurate predictions of species ranges under current and future climate conditions. To date, modelling studies have focused primarily on how changes in long‐term averaged climate conditions are likely to influence species distributions with much less attention paid to the potential effect of extreme events such as droughts and heatwaves which are expected to increase in frequency over coming decades. In this study we explore the benefits of tailoring predictor variables to the specific physiological constraints of species, or groups of species. We show how utilizing spatial predictors of extreme temperature and water availability (heat‐waves and droughts), derived from high‐temporal resolution, long‐term weather records, provides categorically different predictions about the future (2070) distribution of suitable environments for 188 mammal species across different biomes (from arid zones to tropical environments) covering the whole of continental Australia. Models based on long‐term averages‐only and extreme conditions‐only showed similarly high predictive performance tested by hold‐out cross‐validation on current data, and yet some predicted dramatically different future geographic ranges for the same species under 2070 climate scenarios. Our results highlight the importance of accounting for extreme conditions/events by identifying areas in the landscape where species may cope with average conditions, but cannot persist under extreme conditions known or predicted to occur there. Our approach provides an important step toward identifying the location of climate change refuges and danger zones that goes beyond the current standard of extrapolating long‐term climate averages.