Idealized general circulation models (GCMs) suggest global-mean precipitation ceases to increase with warming in hot climates because evaporation is limited by the available solar radiation at the surface. We investigate the extent to which this generalizes in comprehensive GCMs. We find that in the Community Atmosphere Model, global-mean precipitation increases approximately linearly with global-mean surface temperatures up to about 330 K, where it peaks at 5 mm day-1. Beyond 330 K, global-mean precipitation decreases substantially despite increasing surface temperatures because of increased atmospheric shortwave absorption by water vapor, which decreases the shortwave radiation available for evaporation at the surface. Precipitation decreases in the tropics and subtropics but continues to increase in the extratropics because of continuously strengthening poleward moisture transport. Precipitable water increases everywhere, resulting in longer water-vapor residence times and implying more episodic precipitation. Other GCMs indicate global-mean precipitation might exhibit a smaller maximum rate and begin to decrease at lower surface temperatures. Earth's climate has experienced substantial changes over its history, including periods of extremely cold temperatures where most regions contained ice, and periods of extremely warm temperatures where most regions contained no ice. In this study, we explore how precipitation changed in extremely cold and warm climates using a unique set of coupled climate model simulations. We find that global-mean precipitation increases linearly with global-mean surface temperatures up to 330 K, where it peaks at 5 mm day-1 and then decreases as surface temperatures further increase. This occurs because in hot climates, global-mean precipitation is almost entirely balanced by absorbed shortwave radiation at the surface. As the climate warms, the atmosphere contains more water vapor, resulting in increased absorption of shortwave radiation within the atmosphere and decreased absorption of shortwave radiation at the surface. This decreases the energy available for surface evaporation. We show that other climate models exhibit qualitatively similar behavior but indicate global-mean precipitation might exhibit a smaller maximum rate and begin to decrease at lower surface temperatures. These results demonstrate the need to better understand Earth's hydrological cycle in hot climates. These results also have large implications for understanding weathering in past climates and the habitability of other Earth-like planets. In CAM4, global-mean precipitation increases linearly with surface temperatures up to 330 K, then decreases with higher temperatures Precipitation decreases at high temperatures due to increased atmospheric shortwave absorption by water vapor, decreasing surface absorption At high temperatures, precipitation decreases in most regions, but continues to increase in the extratropics due to eddy moisture transport