Extreme weather conditions, like heatwave events, are becoming more frequent with climate change. Animals often modify their behaviour to cope with environmental changes and extremes. During heat stress conditions, individuals change their spatial behaviour and increase the use of shaded areas to assist with thermoregulation. Here, we suggest that for social species, these behavioural changes and ambient conditions have the potential to influence an individual's position in its social network, and the social network structure as a whole. We investigated whether heat stress conditions (quantified through the temperature humidity index) and the resulting use of shaded areas, influence the social network structure and an individual's connectivity in it. We studied this in free‐ranging sheep in the arid zone of Australia, GPS‐tracking all 48 individuals in a flock. When heat stress conditions worsened, individuals spent more time in the shade and the network was more connected (higher density) and less structured (lower modularity). Furthermore, we then identified the behavioural change that drove the altered network structure and showed that an individual's shade use behaviour affected its social connectivity. Interestingly, individuals with intermediate shade use were most strongly connected (degree, strength, betweenness), indicating their importance for the connectivity of the social network during heat stress conditions. Heat stress conditions, which are predicted to increase in severity and frequency due to climate change, influence resource use within the ecological environment. Importantly, our study shows that these heat stress conditions also affect the animal's social environment through the changed social network structure. Ultimately, this could have further flow on effects for social foraging and individual health since social structure drives information and disease transmission.