Ambient sources, including ambient air at dry-bulb and wet-bulb temperature, ground temperature and night sky temperature, were evaluated for their potential to provide space cooling in locations across the U.S. While ground temperature is constant beyond a certain depth, the other sources have fluctuating temperatures, which present intermittent potentials for cooling. Simultaneously, cooling demands also fluctuate with outdoor temperature. Thermal storage can bridge intervals of time during which cooling is needed in the building, but ambient source temperature is too high to provide cooling. The duration of these intervals and the thermal storage capacity required to meet cooling needs based on ambient source potential prior to the interval were quantified for all eleven climate zones across the continental U.S using TMY3 weather data. The thermal storage capacity required to meet the entire annual cooling load is dictated by the span of time without ambient source cooling potential that has the greatest ratio of cooling load to ambient source cooling potential prior to the interval. This maximum thermal storage capacity, normalized by building overall loss coefficient, (this ratio has units of time) was one day or less for night sky temperature for all but the three warmest climates. This ratio was one day or less for wet-bulb temperature for four locations, and for dry-bulb temperature for only two locations. Ground temperature provided continuous cooling potential in all but the three warmest climates, where ground temperature was warmer than the indoor comfort temperature. Because the maximum thermal storage capacity was determined in most climates by uncommon and infrequent coincidence of high cooling demand and low ambient source cooling potential, smaller thermal storage provided substantial cooling capacity in most cases. For instance, ten percent of the maximum supplied 99% of the cooling load for the dry-bulb ambient air source in Albuquerque, and 0.1% of the maximum served over 90% of the cooling load with night sky radiation in New Orleans and Phoenix. While considerable development of hardware and control algorithms to utilize ambient sources for space cooling has occurred, this study shows the potential of these sources to further reduce demands for conventional energy for space cooling across a wide range of climates.