Increases in the severity of heat stress extremes are potentially one of the most impactful consequences of climate change, affecting human comfort, productivity, health, and mortality in many places on Earth. Heat stress results from a combination of elevated temperature and humidity, but the relative contributions of each of these to heat stress changes have yet to be quantified. Here, conditions for the baseline specific humidity are derived for when specific humidity or temperature dominates heat stress changes, as measured using the equivalent potential temperature (theta(E)). Separate conditions are derived over ocean and over land, in addition to a condition for when relative humidity changes make a larger contribution than the Clausius-Clapeyron response at fixed relative humidity. These conditions are used to interpret the theta(E) responses in transient warming simulations with an ensemble of models participating in phase 6 of the Climate Model Intercomparison Project. The regional pattern of theta(E) changes is shown to be largely determined by the pattern of specific humidity changes, with the pattern of temperature changes playing a secondary role. This holds whether considering changes in seasonal-mean theta(E) or in extreme (98th-percentile) theta(E) events, and uncertainty in the response of specific humidity to warming is shown to be the leading source of uncertainty in the theta(E) response at most land locations. Finally, analysis of ERA5 data demonstrates that the pattern of observed theta(E) changes is also well explained by the pattern of specific humidity changes. These results demonstrate that understanding regional changes in specific humidity is largely sufficient for understanding regional changes in heat stress.