Variability of development rate estimates across locations and years using the current heat unit system of growing degree‐days (GDD) with maximum and minimum temperature thresholds of 30 and 10°C (GDD30,10) limits predictability of maturity in hybrid maize (Zea mays L.). Data sets of daily maximum and minimum air temperatures and dates of maize development stages were collected for a range of hybrids at locations in Canada and the northern USA (39° to 45° N lat). Data were analyzed to improve the temperature response functions for maize at different stages of development. Results indicate that during vegetative growth, phenological response to mean daily air temperature followed a sigmoidal curve beginning below 5°C, with maximum response to temperatures between 25 and 30°C. During reproductive growth, the temperature response function was flat from 0 to 12°C and rose significantly only with mean daily air temperatures greater than this range. A general thermal index (GTI) based on these two response functions improved estimation of maturity dates by 50% over estimates made using GDD30,10 (SE of 6.7 d for GTI and 13.6 d for GDD30,10 in estimating time from planting to maturity). The greatest improvement using GTI occurred for the reproductive period (SE of 5.8 d using GTI, compared with 12.1 d using GDD30,10). These results suggest that incorporating the temperature response function reported in this paper would improve prediction of maize development.