High temperature stress at critical growth stages is a major risk factor for wheat in many wheat growing areas globally. Developing weather indices relating to yield reductions in wheat is an urgent requirement for weather-index-based crop insurance. The objectives of the present study were to: (i) identify critical phenological stage(s) for heat stress, (ii) quantify the impact of heat stress at critical growth stage(s) and (iii) work out thresholds of temperature for obtaining above average, average and below average yield of wheat. For achieving these objectives, 11 years’ experimental data for three cultivars (HD-2285, K-8804 and K-9107) under three sowing dates at the Kanpur Centre located in the Indo-Gangetic Plains of Uttar Pradesh, India were used. Among the eight phenological stages, the milk stage (growth stage 73) was identified as most sensitive for high maximum and minimum temperatures to adversely affect yield. The rate of yield reduction with unit increase in maximum and minimum temperatures (°C) was found to be highest in K-8804 and lowest in HD-2285. The optimum ranges of maximum temperature during anthesis, milk, dough and maturity stages are 19·7–21·9, 24·2–26·5, 26·1–28·8 and 29·5–30·8 °C, respectively and those for minimum temperature are 4·3–6·2, 8·3–9·7, 11·5–12·4 and 13·0–15·1 °C, respectively. The thresholds of temperature during critical stages and quantification of heat stress on yield will be of use in devising weather-index-based crop insurance products in wheat and also for breeding temperature-stress-resistant genotypes. This method of devising weather indices in the present study can be used in other crops and regions of the world as an adaptation strategy for climate change.