The objective of this analysis was to use a simple, mechanistic crop growth model to examine the effects of variation in solar radiation and temperature on potential maize (Zea mays L.) yield among locations. Crop phenology and leaf growth were calculated from daily mean temperature data obtained at the five locations studied. Daily biomass accumulation was calculated by estimating the amount of radiation intercepted and assuming maximum crop radiation use efficiency of 1.6 g MJ−1. Grain yield accumulation was simulated using a linear increase in harvest index during grain filling. Observed and simulated grain yields were compared for several sowings at each of five localions ranging from latitude 14°S to 40°N lat. Averaged across sowings, respective observed and simulated oven‐dry grain yields (g m−2) were 816 and 830 at Katherine, Australia; 953 and 908 at Gainesville, FL; 1059 and 1106 at Quincy, FL; 1091 and 1119 at Champaign, IL; and 1580 and 1626 at Grand Junction, CO. Temperature primarily affected growth duration with lower temperature increasing the length of time that the crop could intercept radiation. The solar radiation response was related to the amount of incident radiation and to the fraction of radiation intercepted by the crop. In the tropics (Katherine), high temperature decreased the duration of growth and grain yield, despite high levels of radiation. Only at locations with low temperature and consequent long growth duration. and with high radiation were maize yields simulated to be more than 1600 g m−2 (300 bushels per acre at 15.5% moisture).