The Mars Orbiter Camera onboard the Mars Global Surveyor has obtained several images of polygonal features in the southern polar region. In images taken during the end of the southern spring, when the surrounding surface is free of the seasonal frost, CO2 ice still appears to be present within the polygonal troughs. In Earth's polar regions, polygons such as these are indicative of water ice in the ground below. We analyzed the seasonal evolution of the thermal state and the CO2 content of these features. Our 2-D model includes condensation and sublimation of the CO2 ice, a self consistent treatment of the variations of the thermal properties of the regolith, and the seasonal variations of the local atmospheric pressure which we take from the results of a general circulation model. We find that the residence time of seasonal CO2 ice in troughs depends not only on atmospheric opacity and albedo of the CO2 ice, but also and most significantly on the distribution of water ice in the regolith. Optical properties of the atmosphere and surface CO2 ice can be independently obtained from observations. To date this is not true about the distribution of water ice below the surface. Our analysis quantifies the dependence of the seasonal cycle of the CO2 ice within the troughs on the assumed distribution of the water ice below the surface. We show that presence of water ice in the ground at a depth smaller than the depth of the troughs reduces winter condensation rate of CO2 ice. This is due to higher heat flux conducted from the water ice rich regolith toward the facets of the troughs.