Reducing child mortality is a Sustainable Development Goal, and climate change constitutes numerous challenges for Africa. Previous research has shown an association between leading causes of child mortality and climate change. However, few studies have examined these effects in detail. We aimed to explore the effects of ambient heat on neonate, post-neonate, and child mortality rates. For this pooled time-series analysis, health data were obtained from the International Network for the Demographic Evaluation of Populations and Their Health (INDEPTH) Health and Demographic Surveillance System. We included data from 29 settlements from 13 countries across Africa, collected via monthly surveys from Jan 1, 1993, to Dec 31, 2016. Climate data were obtained from ERA5, collected from Jan 1, 1991, to Dec 31, 2019. We pooled these data for monthly mean daily maximum wet bulb globe temperature (WBGT) and downscaled to geolocations. Due to data heaping, we pooled our health data on a monthly temporal scale and a spatial scale into six different climate regions (ie, Sahel [ie, Burkina Faso and northern Ghana], Guinea [ie, southern Ghana, Côte d’Ivoire, and Nigeria], Senegal and The Gambia, eastern Africa [ie, Kenya, Malawi, Tanzania, Mozambique, and Uganda], South Africa, and Ethiopia). Our outcomes were neonate (ie, younger than 28 days), post-neonate (ie, aged 28 days to 1 year), and child (ie, older than 1 year and younger than 5 years) mortality. To assess the association between WBGT and monthly all-cause mortality, we used a time-series regression with a quasi-Poisson, polynomial-distributed lag model. Between Jan 1, 1993, and Dec 31, 2016, there were 44909 deaths in children younger than 5 years across the 29 sites in the 13 African countries: 10 078 neonates, 14141 post-neonates, and 20 690 children. We observed differences in the association of heat with neonate, post-neonate, and child mortality by study region. For example, for Ethiopia, the relative risk ratio of mortality at the 95th percentile compared with median heat exposure during the study period was 1·14 (95% CI 1·06–1·23) for neonates, 0·99 (0·90–1·07) for post-neonates, and 0·79 (0·73–0·87) for children. Across the whole year, there was a significant increase in the relative risk of increased mortality for children in eastern Africa (relative risk 1·27, 95% CI 1·19–1·36) and Senegal and The Gambia (1·11, 1·04–1·18).