Abstract Children (<5 years) are highly vulnerable during hot weather due to their reduced ability to thermoregulate. There has been limited quantification of the burden of climate change on health in sub-Saharan Africa, in part due to a lack of evidence on the impacts of weather extremes on mortality and morbidity. Using a linear threshold model of the relationship between daily temperature and child mortality, we estimated the impact of climate change on annual heat-related child deaths for the current (1995–2020) and future time periods (2020–2050). By 2009, heat-related child mortality was double what it would have been without climate change; this outweighed reductions in heat mortality from improvements associated with development. We estimated future burdens of child mortality for three emission scenarios (SSP119, SSP245 and SSP585), and a single scenario of population growth. Under the high emission scenario (SSP585), including changes to population and mortality rates, heat-related child mortality is projected to double by 2049 compared to 2005–2014. If 2050 temperature increases were kept within the Paris target of 1.5 °C (SSP119 scenario), approximately 4000–6000 child deaths per year could be avoided in Africa. The estimates of future heat-related mortality include the assumption of the significant population growth projected for Africa, and declines in child mortality consistent with Global Burden of Disease estimates of health improvement. Our findings support the need for urgent mitigation and adaptation measures that are focussed on the health of children.