Climate warming affects biodiversity distribution across all ecosystems. However, beyond changes in species richness, impacts on other biodiversity components are still overlooked, particularly in the marine realm. Here we forecasted the potential effect of climate warming on the phylogenetic and functional components of coastal Mediterranean fish biodiversity. To do so, we used species distribution models to project the potential distribution of 230 coastal fish species by the end of the 21st century based on the IPCC A2 scenario implemented with the Mediterranean climatic model NEMOMED8. From these projections, we assessed the changes in phylogenetic (PD) and functional diversity (FD) of fish assemblages at multiple spatial scales using a dated molecular phylogeny and an extensive functional trait database. At the scale of the entire Mediterranean Sea, the projected extinctions of 40 coastal fish species would lead to a concomitant erosion of PD and FD (13.6 and 3%, respectively). However, a null model revealed that species loss at this scale would not lead to a disproportionate erosion of PD and FD. Similar results were found when considering fish assemblages at the grid cell scale. Indeed, at this scale, the projected changes in species richness would lead to unexpected losses of PD and FD for localized and small areas only. A disproportionate erosion of PD under climate warming was only forecasted when analysing fish assemblages at an intermediate spatial scale, namely the Mediterranean marine ecoregions. Overall, our results emphasize the importance of considering multiple spatial scales when assessing potential impacts of climate warming on the multiple components marine biodiversity.