This paper investigates the consequences of prenatal exposure to hot temperatures on child health in Sub-Saharan Africa (SSA) using a novel indicator of heat waves (the Heat Wave Magnitude Index daily). Leveraging several geo-referenced waves of the Demographic and Health Surveys merged with gridded data on the presence of heat waves and their magnitude since the 1980s, we investigate the effects of inutero exposure to heat waves on several birth and early childhood health outcomes (birth weight, low birth weight, weight-for-age and height-for-age z-scores, undernutrition, severe undernutrition, stunting, severe stunting, anemia). Our analysis demonstrates very robust negative effects on long-term child health, namely the probability that the child is severely stunted. Effects are larger for in-utero shocks experienced in the second and third trimesters of pregnancy and for heat waves of higher intensity. We further show that, at least in the SSA context, adaptation mechanisms such as access to improved water and sanitation, electricity, and improved housing do not appear to significantly attenuate the negative effects of heat waves.