Abstract Multiple studies revealed an effect of climate change on biodiversity by investigating long‐term changes in species distributions and community composition. However, many taxa do not benefit from systematic long‐term monitoring programmes, leaving gaps in our current knowledge of climate‐induced community turnover. We used data extracted from the Global Biodiversity Information Facility to characterize community reorganization under climate change for nine animal taxonomic groups (ants, bats, bees, birds, butterflies, earthworms, frogs, rodents and salamanders), which, for most of them, had never been studied before in this regard. Using a presence‐only community temperature index (CTI), reflecting the relative proportion of warm‐ and cold‐adapted species, we tested whether and how species' assemblages were affected by climate change over the last 30 years. Across Europe and North America, we observed an average increase in CTI, consistent with a gradual species turnover driven by climate change. At the local scale, we could observe that the composition of most species assemblages changed according to temperature variations. However, this change in composition always occurred with a lag compared to climate change, suggesting that communities are experiencing a climatic debt. Results suggest that anthropization may play a role in the decoupling between the change in CTI and the change in local temperature. The results of our study highlight an overall thermophilization of assemblages as a response of temperature warming. We demonstrated that this response may exist for a large range of understudied terrestrial animals, and we introduced a framework that can be used in a broader context, opening new opportunities for global change research.