The thermal inertia of the surface of Mars varies spatially by a factor of 8. This is attributable to changes in the average particle size of the fine material, the surface elevation, the atmospheric opacity due to dust, and the fraction of the surface covered by rocks an fine material. The effects of these nonideal properties on the surface temperatures and derived thermal inertias are modeled, along with the effects of slopes, CO2 condensed onto the surface, and layering of fine material upon solid rock. The nonideal models are capable of producing thermal behavior similar to that observed by the Viking infrared thermal maper, including a morning delay in the postdawn temperature rise and an enhanced cooling in the afternoon relative to any ideal, homogeneous model. The enhanced afternoon cooling observed at the Viking 1 landing site is reproduced by the nonideal models while that atop Arsia Mons volcano is not, but may be attributed to the observing geometry. A histogram of surface thermal inertia versus elevation shows at least two distinct classes: a single region near Amazonis Planitia has low inertias at low elevation; many of the remaining data show an anticorrelation between inertia and elevation, expected because of the change in thermal inertia produced by changes in the atmospheric pressure an dust opacity with elevation.