The heat index is a widely used measure of apparent temperature that accounts for the effects of humidity using Steadman's model of human thermoregulation. Steadman's model, however, gives unphysical results when the air is too hot and humid or too cold and dry, leading to an undefined heat index. For example, at a relative humidity of 80%, the heat index is only defined for temperatures in the range of 288-304 K (59 degrees-88 degrees F). Here, Steadman's thermoregulation model is extended to define the heat index for all combinations of temperature and humidity, allowing for an assessment of Earth's future habitability. The extended heat index can be mapped onto physiological responses of an idealized human, such as heat exhaustion, heat stroke, and even heat death, providing an indication of regional health outcomes for different degrees of global warming. Significance StatementThe existing heat index is well-defined for most combinations of high temperature and humidity experienced on Earth in the preindustrial climate, but global warming is increasingly generating conditions for which the heat index is undefined. Therefore, an extension of the original heat index is needed. When extending the heat index, we use the same physiological model as in the original work of Steadman to ensure backward compatibility. Following Steadman, each value of the heat index is mapped onto a measurable physiological variable, which can be useful for assessing the health impacts of various combinations of temperature and humidity, especially for outdoor workers.