Heat waves have pronounced impacts on human health, ecosystems, and society. Heat waves have become more frequent and intense globally and are likely to intensify further in a warming climate. Across the United States there is a warming trend in average surface temperatures, but concordant increase in heat wave severity appears absent. Limitations in heat waves studies may be responsible for limited detection of a heat wave warming signal. We track daily spatiotemporal evolution of heat waves using geometric concepts and clustering algorithms to investigate how heat manifests on the land surface. We develop a spatial metric combining heat wave frequency, magnitude, duration, and areal extent. We find mixed trends in some individual heat wave characteristics across the United States during 1981-2018. However, exploration of the spatiotemporal evolution of combined heat wave characteristics shows considerable increases during this period and indicates a substantial increase in heat wave hazard across the United States.