This research was conducted in order to assess the impact that climate change has on the demands for heating and cooling energy in hospitals in six cities located in six countries in the Indian Ocean region. Three scenarios (B1, A1B, and A2) of the Intergovernmental Panel on Climate Change (IPCC) were applied in the undertaking of this work. The hourly outdoor data relating to air temperature, wind speed, relative humidity, radiation, and atmospheric pressure recorded over the last 30 years were used as inputs by Meteonorm software to enable the forecasting. The averages obtained in all the 18 models used in the IPCC report 2007 were included in the Meteonorm software and applied for assessing the future climate. The Energy-Plus software was used for assessing the thermal performance of hospitals under natural ventilation, then the energy demand during five periods (past, current, 2030, 2060, and 2090). Thermal insulation was utilized as a passive strategy for reducing cooling and heating energy consumption in the hospitals. Results showed that the use of an envelope of thermal insulation in hospitals was one of the solutions that allowed a reduction in the energy consumption for cooling and heating while increasing the thermal comfort within the hospital. Moreover, by 2090, the ventilation system was recommended in all these hospitals for improving the quality of indoor air, since the heat rate was very high. In the cases of the six islands in the Indian Ocean, each of them represented by one city, the annual energy demand for cooling will increase between 17.1 and 25.4% by 2030; 34.6 and 50.2% by 2060; and 60.8 and 95.1% by 2090. With the use of passive design as a strategy, the annual mean thermal performance of hospitals is predicted to increase to 184% by 2060, while 40% of the cost of cooling energy will be saved. Despite this, the outdoor climate will be 5% harsher in Victoria than in other cities by the year 2090.