In the face of climate change, the life history traits of large terrestrial mammals will prevent them from adapting genetically at a sufficient pace to keep track with changing environments, and habitat fragmentation will preclude them from shifting their distribution range. Predicting how habitat-bound large mammals will respond to environmental change requires measurement of their sensitivity and exposure to changes in the environment, as well as the extent to which phenotypic plasticity can buffer them against the changes. Behavioural modifications, such as a shift to nocturnal foraging or selection of a cool microclimate, may buffer free-living mammals against thermal and water stress, but may carry a cost, for example by reducing foraging time or increasing predation risk. Large mammals also use physiological responses to buffer themselves against changing environments, but those buffers may be compromised by a changing physical environment. A decrease in the available food energy or water leads to a trade-off in which the precision of homeothermy is relaxed, resulting in large daily fluctuations in body temperature. Understanding how large mammals prioritise competing homeostatic systems in changing environments, and the consequences of that prioritisation for their fitness, requires long-term monitoring of identifiable individual animals in their natural habitat. Although body size predicts general ecological and energetic patterns of terrestrial mammals, high intraspecific and interspecific variability means that a species-directed approach is required to accurately model responses of large mammals to climate change.