Transient eddies in the extratropical storm tracks are a primary mechanism for the transport of momentum, energy, and water in the atmosphere, and as such are a major component of the climate system. Changes in the extratropical storm tracks under global warming would impact these transports, the ocean circulation and carbon cycle, and society through changing weather patterns. I show that the southern storm track intensifies in the multimodel mean of simulations of 21st century climate change, and that the seasonal cycle of storm-track intensity increases in amplitude in both hemispheres. I use observations of the present-day seasonal cycle to confirm the relationship between storm-track intensity and the mean available potential energy of the atmosphere, and show how this quantitative relationship can be used to account for much of the varied response in storm-track intensity to global warming, including substantially different responses in simulations with different climate models. The results suggest that storm-track intensity is not related in a simple way to global-mean surface temperature, so that, for example, a stronger southern storm track in response to present-day global warming does not imply it was also stronger in hothouse climates of the past.