Kurihara, Y., 1971: Seasonal variation of temperature in an atmosphere at rest. Journal of the Meteorological Society of Japan, 49, Special Issue (Dec), 537-544.

Abstract: The variation of temperature of an atmosphere at rest with latitude and time is investigated. The heating of an air column which is due to short-wave and long-wave radiation is estimated by simple parameterization. A condition of heat balance is assumed at the earth's surface to evaluate sensible heat flux there.
An analysis of the equation shows that the heat capacity and the properties of the long-wave radiation of the atmosphere determine the time lag between variations in temperature and insolation. In the numerical integration, extreme temperatures at middle latitude occurred about one month after the solstices. In the equatorial region, two maxima and two minima appeared in the temperature variation. The lowest temperature in the polar region took place in spring because of the winter polar night.
A comparison of the results of the integration with the observed variation demonstrates the importance of the meridional transport of energy in the atmosphere and ocean. This comparison also suggests the importance of the storage of energy in the ocean and land.