Many studies project that climate change is expected to cause a significant number of excess deaths. Yet, in integrated assessment models that determine the social cost of carbon (SCC), human mortality impacts do not reflect the latest scientific understanding. We address this issue by estimating country-level mortality damage functions for temperature-related mortality with global spatial coverage. We rely on projections from the most comprehensive published study in the epidemiology literature of future temperature impacts on mortality (Gasparrini et al. in Lancet Planet Health 1:e360–e367, 2017), which estimated changes in heat- and cold-related mortality for 23 countries over the twenty-first century. We model variation in these mortality projections as a function of baseline climate, future temperature change, and income variables and then project future changes in mortality for every country. We find significant spatial heterogeneity in projected mortality impacts, with hotter and poorer places more adversely affected than colder and richer places. In the absence of income-based adaptation, the global mortality rate in 2080–2099 is expected to increase by 1.8% [95% CI 0.8–2.8%] under a lower-emissions RCP 4.5 scenario and by 6.2% [95% CI 2.5–10.0%] in the very high-emissions RCP 8.5 scenario relative to 2001–2020. When the reduced sensitivity to heat associated with rising incomes, such as greater ability to invest in air conditioning, is accounted for, the expected end-of-century increase in the global mortality rate is 1.1% [95% CI 0.4–1.9%] in RCP 4.5 and 4.2% [95% CI 1.8–6.7%] in RCP 8.5. In addition, we compare recent estimates of climate-change induced excess mortality from diarrheal disease, malaria and dengue fever in 2030 and 2050 with current estimates used in SCC calculations and show these are likely underestimated in current SCC estimates, but are also small compared to more direct temperature effects.