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. Leveraging a saturated fixed-effects model that controls for annual trends and location-specific seasonality, and that allows the impacts of temperature to vary non-parametrically while rainfall and humidity have flexible non-linear forms, we find that extreme heat and humidity in the month of birth exert significant negative effects on children's nutritional status as measured by mid upper arm circumference. The impact of humidity in particular persists when child, mother and household controls are included. We find that exposure to changing climate in utero and in the month of conception also matters. Possible explanations for our findings include consequences of varying heat, humidity, and rainfall on the extent of pasture, rain-fed and irrigated lands, on the propensity of household out-migration, and on mother's age at first marriage. We employ alternate models and undertake falsification tests to underline the robustness of the estimates. Our results indicate that climate change has real consequences for the health of very young populations who are in vulnerable areas.