This study uses panel data for 39 years and 13 districts to estimate the yield sensitivity of major food crops to climate change in the South Indian state of Tamil Nadu. First estimate the marginal impacts of climate variables on crop yield using Panel Corrected Standard Error (PCSE) models. These estimates are then used to identify yield sensitivities in the future based on projected climate variables from the Regional Climate Model version 4 (RegCM4). Empirical results show a quadratic (inverted U shaped) relationship between rice and sorghum yield and climate variables. As temperature and rainfall increase, crop yield initially increases up to a threshold level, and then decreases. Following the RegCM4 projections that observed warming and anomalies in rainfall will continue, this could result in a significant loss in crop productivity. Projections suggest that there may be a 10 percent decline in rice yield and 9 percent decline in sorghum yield by the end of the 21st century relative to average yields during 1971-2009. This indicates a need for new seed varieties that are less sensitive to rainfall and temperature thresholds, and, adaptation practices such as adjustments in sowing time.