The objective of this study is to evaluate the influence that minimum temperature, average temperature, and maximum temperature have on yield when using the iGAEZ model. Simulated yields on each grid cell for 1980–1999, in three leading producers of wheat, rice and maize, were combined with climate datasets to evaluate the relationships between temperature and simulated crop yields. A generalized additive model was evaluated to analyse changes in diurnal temperature range (DTR) and crop yields. Results differ depending on crop and region as to whether there was a clear positive/negative response of yields to daily temperature indices (DTIs) (including DTR, Tmax, Tmin and Tave). However, the effects of DTIs were statistically significant using a generalized additive model for all crops and regions. To evaluate whether future changes in DTIs are relevant for impact assessment, yield responses to projected changes in DTIs by 2080–2099, from 19 climate models under SRES A2, B1 scenarios, were estimated. Among DTIs, DTR changes did significantly affect yield responses in several cases, such as in maize and rice yields in South Asia under B1 scenario. The decreasing/increasing trend of DTIs has an important implication for estimating the future impact of climate changes. Copyright © 2012 John Wiley & Sons, Ltd.