Climate change threatens livestock productivity primarily through heat stress, the combined physiological burden of elevated temperatures and atmospheric moisture. Existing empirical studies commonly rely on scalar composite indices such as the Temperature–Humidity Index (THI), which impose restrictive functional forms, cannot capture nonlinear or asymmetric joint responses to temperature and humidity, and may underestimate the effects of cold and dry weather. This study introduces a twodimensional Chebyshev polynomial framework that flexibly models the joint distribution of temperature and atmospheric moisture and its effects on livestock productivity. Applying this framework to state-level U.S. data from 1980 to 2024, we estimate climate effects on eight outcomes spanning major livestock types and production stages: cattle weight, calf survival rates, hog weight, piglet survival rates, litter size, broiler weight, rate of lay, and milk production per cow. Results reveal that early-life outcomes, such as calf and piglet survival rates, are markedly less sensitive to temperature–humidity stress than adult weight or output measures. Poultry outcomes are relatively stable, consistent with the buffering role of climate-controlled housing. Future projections indicate that hog weight, cattle weight, and milk yield will experience the largest losses, especially in summer and in the Southeast, where heat-stress exposure is projected to increase.
