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This paper studies the impact of climate change on the nutritional status of very young children between the ages of 0-3 years by using weather data from the last half century merged with rich information on child, mother, and household characteristics in rural coastal Bangladesh. We evaluate the health consequences of rising temperature and relative humidity and varying rainfall jointly employing alternate functional forms. Leveraging models that control for annual trends and location-specific seasonality, and that allow the impacts of temperature to vary non-parametrically while rainfall and humidity have flexible non-linear forms, we find that temperatures that exceed 25 °C (the "comfortable" benchmark) in the month of birth exert negative effects on children's nutritional status as measured by mid upper arm circumference. Humidity has a positive impact which persists when child, mother and household controls are included. We find that exposure to changing climate in utero also matters. Explanations for these results include consequences of weather fluctuations on the extent of pasture, cropland, and rainfed lands planted with rice and other crops, and on mother's age at first marriage. Our results underline that climate change has real consequences for the health of very young populations in vulnerable areas.