Extreme heat events are likely to become more frequent in the coming decades due to climate change.  Exposure to extreme heat depends not only on changing climate, but also on changes in the size and spatial distribution of the human population.  Here we provide a new projection of population exposure to extreme heat for the continental United States that takes into account both of these factors.   Using projections from a suite of regional climate models driven by global climate models and forced with the SRES A2 scenario and a spatially explicit population projection consistent with the socioeconomic assumptions of that scenario, we project changes in exposure into the latter half of the 21^st century.  We find that US population exposure to extreme heat increases four- to six-fold over observed levels in the late 20^th century, and that changes in population are as important as changes in climate in driving this outcome.  Aggregate population growth, as well as redistribution of the population across larger US regions, strongly affects outcomes while smaller-scale spatial patterns of population change have smaller effects.  The relative importance of population and climate as drivers of exposure varies across regions of the country.