Solid-state lasers have held great promise for the generation of high-average-power, high-quality output beams for a number of decades. However, the inherent difficulty of scaling the active solid-state gain media while continuing to provide efficient cooling has limited demonstrated powers to <5kW. We have developed and demonstrated a new operational mode for solid-state laser systems in which the cooling of the gain medium is separated in time from the lasing cycle. In heat-capacity operation, no cooling takes place during lasing. The gain medium is pumped very uniformly and the waste heat from the excitation process is stored in the solid-state gain medium. By depositing the heat on time scales that are short compared to thermal diffusion across the optical aperture, very high average power operation is possible while maintaining low optical distortions.