We investigate the risks presented by heat waves for adverse health conditions for babies and expectant mothers when these mothers have been exposed to heat waves during gestation or during the period just prior to conception. Rather than just birth weight and gestational age, we focus on less common metrics such as abnormal conditions in the newborn (fetal distress, reliance on a ventilator, and meconium aspiration) and adverse health conditions in the mother (pregnancy-related hypertension, uterine bleeding during pregnancy, eclampsia, and incompetent cervix). We use monthly panel data for over 3,000 U.S. counties, constructed from the confidential version of the U.S. Natality Files for 1989-2008. Our models control for sociodemographic factors and include county, month, and state-by-year fixed effects to control for unobserved spatial and timewise heterogeneity in the data. Even within the United States, where there is widespread access to air conditioning, heat waves increase the fraction of babies with abnormal conditions related to maternal stress, as well as the fraction of mothers who experience pregnancy-related adverse health conditions. The scope for these risks in developing countries is likely to be even greater.