Heat stress accumulates in the human body when a person is exposed to a thermal condition for a long time. Considering this fact, we have defined the accumulated heat stress (AH) and have developed the accumulated heat stress index (AHI) to quantify the strength of heat stress. AH represents the heat stress accumulated in a 72-h period calculated by the use of a time-weighted function, and the AHI is a standardized index developed by the use of an equiprobability transformation (from a fitted Weibull distribution to the standard normal distribution). To verify the advantage offered by the AHI, it was compared with four thermal indices the humidex, the heat index, the wet-bulb globe temperature, and the perceived temperature used by national governments. AH and the AHI were found to provide better detection of thermal danger and were more useful than other indices. In particular, AH and the AHI detect deaths that were caused not only by extremely hot and humid weather, but also by the persistence of moderately hot and humid weather (for example, consecutive daily  aximum temperatures of 28–32 °C), which the other indices fail to detect.