Abstract The spatial and temporal distribution of stable and convectively neutral air masses is examined in climate simulations with carbon dioxide levels spanning from modern-day values to very high levels that produce surface temperatures relevant to the hottest climate of the past 65 million years. To investigate how stability with respect to slantwise and upright moist convection changes across a wide range of climate states, the condition of moist convective neutrality in climate experiments is assessed using metrics based upon the saturation of potential vorticity, which is zero when temperature profiles are moist adiabatic profiles along vortex lines. The modern climate experiment reproduces previously reported properties from reanalysis data, in which convectively neutral air masses are common in the tropics and locally at higher latitudes, especially over midlatitude continents in summer and ocean storm tracks in winter. The frequency and coverage of air masses with higher stabilities declines in all seasons at higher latitudes with warming; the hottest case features convectively neutral air masses in the Arctic a majority of the time in January and nearly universally in July. The contribution from slantwise convective motions (as distinct from upright convection) is generally small outside of midlatitude storm tracks, and it declines in the warmer climate experiments, especially during summer. These findings support the conjecture that moist adiabatic lapse rates become more widespread in warmer climates, providing a physical basis for using this assumption in estimating paleoaltimetry during warm intervals such as the early Eocene.