Rising sea temperatures are likely to increase the frequency of disease outbreaks affecting reef-building corals through impacts on coral hosts and pathogens. We present and compare climate model projections of temperature conditions that will increase coral susceptibility to disease, pathogen abundance and pathogen virulence. Both moderate (RCP 4.5) and fossil fuel aggressive (RCP 8.5) emissions scenarios are examined. We also compare projections for the onset of disease-conducive conditions and severe annual coral bleaching, and produce a disease risk summary that combines climate stress with stress caused by local human activities. There is great spatial variation in the projections, both among and within the major ocean basins, in conditions favouring disease development. Our results indicate that disease is as likely to cause coral mortality as bleaching in the coming decades. These projections identify priority locations to reduce stress caused by local human activities and test management interventions to reduce disease impacts.