Air temperature and humidity have a great impact on public health, leads to heat stress. The US National Weather Service uses temperature and relative humidity to build a heat index (HI) as a metric to identify the thresholds for heat stress as felt by the public. Under climate change conditions and especially in hot humid weather during summer, the number of hot days in Hanoi has increased in recent times. Subsequently, the heat index is rising in both number of occurrences and level of intensity leading to increasing temperature stress on people's health. The daily heat index for the future was simulated using maximum daily temperature and minimum daily relative humidity based on climate change scenarios. Maximum daily temperature was provided by the climate change model, while minimum daily relative humidity was estimated from the following: maximum daily temperature, mean daily temperature and daily rainfall. Results show that in the future, the heat index will increase by 0.0777 degrees C/year in the RCP 4.5 scenario and 0.08 degrees C/year in the RCP 8.5 scenario. Number of weeks with heat at danger tends to increase to 5.5 weeks/5 year for scenario RCP 4.5, and it is 6 weeks/5 years under RCP 8.5 scenario. In particular, the number of days of heatstroke over a 30-year period (from 1991 to 2020) amounted to only 4, that is an average of 0.13 days of the year, which represents a very rare weather phenomenon in the past. In contrast, under an RCP 4.5 scenario in the future over a 30-year period, the average number of days per year will be 2, 57 days; while the average number of days per year under an RCP 8.5 scenario would be 3, 87 days. This phenomenon will be mainly concentrated in the months of June, July, and August. Projections of this type are a key tool for communities working out how they will adapt to heat stress in the context of climate change.