Motivated by growing heat-related morbidity and mortality in a warming climate, this paper assesses global heat health risk in order to understand the challenges to sustainability in the 21st century, using four Representative Concentration Pathways (RCPs) of the HadGEM2-ES climate model and five Shared Socio-Economic Pathways (SSPs). Factors influencing global heat health risk were reviewed and risks were estimated based on heat hazard and socio-economic vulnerability. Hazard, vulnerability, risk and in particular, populations at different risk levels, were analyzed quantitatively at both global and regional scales. The results show that under an RCP8.5-SSP3 scenario, the world will be subject to the highest heat health risk, with rapidly increasing hazard levels and vulnerability over the century. Less developed or developing regions, such as Africa and Southeast Asia, are at the highest risk. The heat risk under an RCP2.6-SSP1 scenario will first increase and then fall, resulting in the lowest heat-health-risk pattern. We found that heat health risk will increase during the century under all RCP-SSP scenarios, with a higher frequency, higher intensity, longer duration and expanding spatial reach. Significant differences were observed across regions. The results make clear that the increasing risk poses significant challenges to sustainable human health. To meet these challenges, more attention and effective actions are urgently needed from both policy makers and individuals.