Alpine large herbivores have developed physiological and behavioural mechanisms to cope with fluctuations in climate and resource availability that may become maladaptive under climate warming. We tested this hypothesis in female Alpine ibex (Capra ibex) by modelling annual and daily movement and activity patterns in relation to temperature, vegetation productivity and reproductive status based on bio-logging data and climate change projections. In summer, ibex moved upslope, tracking the green wave. Ibex decreased diel activity sharply above a threshold temperature of 13-14 degrees C, indicating thermal stress, but compensated behaviourally by foraging both earlier and later in the day, and by moving further upslope than on cooler days, especially reproductive females. This critical temperature will be exceeded three times as often under climate change projections. Under such scenarios, the altitudinal extent of the area will limit the available habitat providing thermal shelter, potentially impacting performance and population distribution of this emblematic mountain ungulate.