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Most species-climate models relate range margins to long-term mean climate but lack mechanistic understanding of the ecological or demographic processes underlying the climate response. We examined the case of a climatically limited edge-of-range population of a medium-sized grassland bird, for which climate responses may involve a behavioural trade-off between temperature stress and reproduction. We hypothesised that temperature will be a limiting factor for the conspicuous, male snort-call display behaviour, and high temperatures would reduce the display activity of male birds. Using remote tracking technology with tri-axial accelerometers we classified and studied the display behaviour of 17 free-ranging male little bustards, Tetrax tetrax, at 5 sites in the Iberian Peninsula. Display behaviour was related to temperature using two classes of Generalized Additive Mixed Models (GAMMs) at different temporal resolutions. GAMMs showed that temperature, time of the day and Julian date explained variation in display behaviour within the day, with birds snort-calling significantly less during higher temperatures. We also showed that variation in daily snort-call activity was related to average daytime temperatures, with our model predicting an average decrease in daytime snort-call display activity of up to 10.4% for the temperature increases projected by 2100 in this region due to global warming. For lekking birds and mammals undertaking energetically-costly displays in a warming climate, reduced display behaviour could impact inter- and intra-sex mating behaviour interactions through sexual selection and mate choice mechanisms, with possible consequences on mating and reproductive success. The study provides a reproducible example for how accelerometer data can be used to answer research questions with important conservation inferences related to the impacts of climate change on a range of taxonomic groups.