Heat stress is one of the major wheat (Triticum aestivum) production constraints in South Asia (SA), particularly in the Eastern Gangetic Plains (EGP) of India and Bangladesh. Malnutrition is also a severe problem among children and women in SA. Wheat varieties with high grain Zn/Fe are a sustainable, cost-effective solution in the fight against hidden hunger. Thirty wheat genotypes were characterised under the optimum temperature and heat stress conditions in 2016–2017 and 2017–2018 to study the response of the stress on the yield, physiological traits and grain Zn/Fe content. A significant genetic variation was observed for all the traits under the optimum temperature and stress conditions. The yield was reduced by an average of 59.5% under heat stress compared to that of the optimum temperature. A strong positive association of the canopy temperature depression (CTD) with the grain yield (GY) was observed under the heat stress. A negative correlation of the grain Zn/Fe with the yield was observed under the optimum temperature and heat stress conditions, while the association between the grain Zn and Fe was positive. The genotypes BRW 3723, BRW 3759, BRW 3797, BRW 160, HD 2967, HD 2640 were found to be heat-tolerant in both years. Among the tolerant genotypes, BRW 934, BRW 3807 and BRW 3804 showed a high zinc content and BRW 934, BRW 3797, BRW 3788 and BRW 3807 showed a high iron content, respectively. These genotypes can be explored in future breeding programmes to address the problem of nutritional deficiency.