We analyze the impact of in utero temperature exposure on the birth weight and prevalence of low birth weight using administrative data on singleton live births conceived between 2000 and 2016 in Hungary. We find that exposure to high temperatures during pregnancy decreases birth weight, but its impact on the probability of low birth weight is weaker. Exposure to one additional hot day (mean temperature >25°C) during the gestation period reduces birth weight by 0.5 grams. The second and third trimesters appear to be slightly more sensitive to temperature exposure than the first trimester. We project that climate change will decrease birth weight and increase the prevalence of low birth weight by the mid-21st century. The projected impacts are the strongest for newborns conceived during the winter and spring months.