Heat waves give rise to order of magnitude higher mortality rates than other weather-related natural disasters. Unfortunately both the severity and amplitude of heat waves are predicted to increase worldwide as a consequence of climate change. Hence, meteorological services have a growing need to identify such periods in order to set alerts, whilst researchers and industry need representative future heat waves to study risk. This paper introduces a new location-specific mortality risk focused definition of heat waves and a new mathematical framework for the creation of time series that represents them. It focuses on identifying periods when temperatures are high during the day and night, as this coincidence is strongly linked to mortality. The approach is tested using observed data from Brazil and the UK. Comparisons with previous methods demonstrate that this new approach represents a major advance that can be adopted worldwide by governments, researchers and industry.