Climate change is expected to have profound, partly unforeseeable effects on the composition of functional traits of complex ecosystems, such as coral reefs, and some ecosystem properties are at risk of disappearing. This study applies a novel spatially explicit, individual-based model to explore three critical life history traits of corals: heat tolerance, competitiveness and growth performance under various environmental settings. Building upon these findings, we test the adaptation potential required by a coral community in order to not only survive but also retain its diversity by the end of this century under different IPCC climate scenarios. Even under the most favourable IPCC scenario (Representative Concentration Pathway, RCP 2.6), model results indicate that shifts in the trait space are likely and coral communities will mainly consist of small numbers of temperature-tolerant and fast-growing species. Species composition of coral communities is likely to be determined by heat tolerance, with competitiveness most likely playing a subordinate role. To sustain ~15% of current coral cover under a 2 °C temperature increase by the end of the century (RCP 4.5), coral systems would have to accommodate temperature increases of 0.1-0.15 °C per decade, assuming that periodic extreme thermal events occurred every 8 years. These required adaptation rates are unprecedented and unlikely, given corals' life-history characteristics.