The radiative cooling rate in the tropical upper troposphere is expected to increase as climate warms. Since the tropics are approximately in radiative-convective equilibrium (RCE), this implies an increase in the convective heating rate, which is the sum of the latent heating rate and the eddy heat flux convergence. We examine the impact of these changes on the vertical profile of cloud ice amount in cloud-resolving simulations of RCE. Three simulations are conducted: a control run, a warming run, and an experimental run in which there is no warming but a temperature forcing is imposed to mimic the warming-induced increase in radiative cooling. Surface warming causes a reduction in cloud fraction at all upper tropospheric temperature levels but an increase in the ice mixing ratio within deep convective cores. The experimental run has more cloud ice than the warming run at fixed temperature despite the fact that their latent heating rates are equal, which suggests that the efficiency of latent heating by cloud ice increases with warming. An analytic expression relating the ice-related latent heating rate to a number of other factors is derived and used to understand the model results. This reveals that the increase in latent heating efficiency is driven mostly by 1) the migration of isotherms to lower pressure and 2) a slight warming of the top of the convective layer. These physically robust changes act to reduce the residence time of ice along at any particular temperature level, which tempers the response of the mean cloud ice profile to warming.