With the ongoing rise in global average temperatures, animals are expected to increasingly dedicate their time and energy to thermoregulation. In response to high temperatures, animals typically either seek for and move into thermal refuges, or reduce their activity during the hottest hours of the day. Yet, the often lower resource availability in thermal refuges, combined with the reduction of foraging activity, may create indirect energetic costs of behavioural thermoregulation, forcing individuals to further adjust their behaviours under different spatial contexts. To elucidate such complex behavioural responses of individuals living in different landscapes, we studied how alpine chamois behaviour (Rupicapra rupicapra), a cold-adapted endotherm, varied in relation to both temperature and within-home range access to thermal refuges. We used Hidden Markov Models to analyse individual time-budgets and daily habitat use of 26 GPS-tagged females monitored during summer in the French Alps. Females showed heat stress avoidance behaviours above a threshold temperature of 17.8°C, increasing the use of forest and northern slopes by 2.8% and 2.2%, respectively, for each 1°C increase in temperature. Individuals with access to forests also increased daily time spent foraging, while individuals with access to northern slopes increased the time spent relocating at the expense of foraging. Including local landscape context and jointly analysing resource selection and behavioural activity is hence key for improved insights into nuanced changes in individual responses to climate change in different spatial contexts, providing also an improved evidence base for wildlife managers to identify and protect key thermal cover habitats.