Convective available potential energy (CAPE) is shown to increase rapidly with warming in simulations of radiative-convective equilibrium over a wide range of surface temperatures. The increase in CAPE implies a systematic deviation of the thermal stratification from moist adiabatic that is non-negligible at high temperatures. However, cloud buoyancy remains much smaller than what CAPE would imply because entrainment is more effective in reducing buoyancy in warmer atmospheres. An entraining plume model in the limit of zero cloud buoyancy is shown to reproduce the increase in CAPE with warming if the entrainment rate is held fixed and increases in the vertical extent of convection are taken into account. These model results together with radiosonde observations are used to support a conceptual model in which entrainment plays a role in determining the thermal stratification of the tropical atmosphere.