The Paris Agreement settled to limit global warming to 2°C and possibly 1.5°C from pre-industrial times. However, little is known about the implications of such climatic goals for biodiversity once species' adaptability to new climatic conditions is accounted for. Here, we projected the bioclimatic space loss for mammalian communities across terrestrial biomes, under four alternative emission scenarios to year 2050, and evaluated the risk for taxonomic, phylogenetic, and functional biodiversity in each biome. The high-emission scenario (largely overshooting Paris limits) will lead to an average 34% bioclimatic space loss across biomes, surpassing critical levels in half of them (31 out of 63), including six biomes with high biodiversity content. Overall, these biomes account for an area at risk which is 10 times larger compared to that identified under low-emission scenarios. Under intermediate-emission scenario the loss is reduced to 28%, but two biomes with high biodiversity content will still be at risk. Achieving the 1.5°C target would reduce the average bioclimatic space loss to 19%, with only eight biomes facing critical levels of loss, none of which hosts high biodiversity content. These results highlight the biological risk of climate inaction and the consequences of exceeding Paris Agreement's climatic goals.