Growing evidence suggests that extreme heat events affect both pregnant women and their infants, but few studies are available from sub-Saharan Africa. Using data from 138,015 singleton births in 16 hospitals in Benin, Malawi, Tanzania and Uganda, we investigated the association between extreme heat and early perinatal deaths, including antepartum and intrapartum stillbirths, and deaths within 24 h after birth using a time-stratified case–crossover design. We observed an association between an increase from the 75th to the 99th percentile in mean temperature 1 week (lag 0–6 d) before childbirth and perinatal mortality (odds ratio (OR) = 1.34 (95% confidence interval (CI) 1.01–1.78)). The estimates for stillbirths were similarly positive, but CIs included unity: OR = 1.29 (95% CI 0.95–1.77) for all stillbirths, OR = 1.18 (95% CI 0.71–1.95) for antepartum stillbirths and OR = 1.64 (95% CI 0.74–3.63) for intrapartum stillbirths. The cumulative exposure–response curve suggested that the steepest slopes for heat for intrapartum stillbirths and associations were stronger during the hottest seasons. We conclude that short-term heat exposure may increase mortality risks, particularly for intrapartum stillbirths, raising the importance of improved intrapartum care.