Radiative heating of clouds, particularly those in the upper troposphere, alters temperature gradients in the atmosphere, affecting circulation and precipitation in today's and future climates. However, the response of cloud radiative heating to global warming remains largely unknown. We study changes to high cloud radiative heating in a warmer climate, identify physical mechanisms responsible for these changes, and develop a theory based on well-understood physics to predict them. Our approach involves a stepwise procedure that builds upon a simple hypothesis of an upward shift in cloud radiative heating at constant temperature and gradually incorporates additional physics. We find that cloud radiative heating intensifies as clouds move upward, suggesting that the role of high clouds in controlling atmospheric circulations increases in a warmer climate.