The phase change of water from liquid to vapor is one of the most energy-intensive physical processes in nature, giving it immense potential for cooling. Diverse evaporative cooling strategies have resulted worldwide, including roof ponds and sprinklers, courtyard fountains, wind catchers with qanats, irrigated green roofs, and fan-assisted evaporative coolers. These methods all require water in bulk liquid form. The evaporation of moisture that has been sorbed from the atmosphere by hygroscopic materials is equally energy-intensive, however, yet has not been examined for its cooling potential. In arid and semi-arid climates, hygroscopic earth buildings occur widely and are known to maintain comfortable indoor temperatures, but evaporation of moisture from their walls and roofs has been regarded as unimportant since water scarcity limits irrigation and rainfall; instead, their cool interiors are attributed to well-established mass effects in delaying the transmission of sensible gains. Here, we investigate the cooling accomplished by daily cycles of moisture sorption and evaporation which, requiring only ambient humidity, we designate as "intrinsic" evaporative cooling. Connecting recent soil science to heat and moisture transport studies in building materials, we use soils, adobe, cob, unfired earth bricks, rammed earth, and limestone to reveal the effects of numerous parameters (temperature and relative humidity, material orientation, thickness, moisture retention properties, vapor diffusion resistance, and liquid transport properties) on the magnitude of intrinsic evaporative cooling and the stabilization of indoor relative humidity. We further synthesize these effects into concrete design guidance. Together, these results show that earth buildings in diverse climates have significant potential to cool themselves evaporatively through sorption of moisture from humid night air and evaporation during the following day's heat. This finding challenges the perception of limited evaporative cooling resources in arid climates and greatly expands the applicability of evaporative cooling in contemporary buildings to water-stressed regions.