The altitudinal shifts of many montane populations are lagging behind climate change. Understanding habitual, daily behavioural rhythms, and their climatic and environmental influences, could shed light on the constraints on long-term upslope range-shifts. In addition, behavioural rhythms can be affected by interspecific interactions, which can ameliorate or exacerbate climate-driven effects on ecology. Here, we investigate the relative influences of ambient temperature and an interaction with domestic sheep (Ovis aries) on the altitude use and activity budgets of a mountain ungulate, the Alpine chamois (Rupicapra rupicapra). Chamois moved upslope when it was hotter but this effect was modest compared to that of the presence of sheep, to which they reacted by moving 89–103 m upslope, into an entirely novel altitudinal range. Across the European Alps, a range-shift of this magnitude corresponds to a 46% decrease in the availability of suitable foraging habitat. This highlights the importance of understanding how factors such as competition and disturbance shape a given species’ realised niche when predicting potential future responses to change. Furthermore, it exposes the potential for manipulations of species interactions to ameliorate the impacts of climate change, in this case by the careful management of livestock. Such manipulations could be particularly appropriate for species where competition or disturbance already strongly restricts their available niche. Our results also reveal the potential role of behavioural flexibility in responses to climate change. Chamois reduced their activity when it was warmer, which could explain their modest altitudinal migrations. Considering this behavioural flexibility, our model predicts a small 15–30 m upslope shift by 2100 in response to climate change, less than 4% of the altitudinal shift that would be predicted using a traditional species distribution model-type approach (SDM), which assumes that species’ behaviour remains unchanged as climate changes. Behavioural modifications could strongly affect how species respond to a changing climate.