"Heat always moves from places of higher density of heat to places of lower density of heat, thus states the Second Law of Thermodynamics (Van Ness. 1969. Page 54). In daylight, air is always colder than soil; consequently, heat is transferred from the soil to the air, not vice versa."

The heat from a CO2 molecule to another molecule within the air will not increase the heat of the air. As we seem to have established here, the CO2 will cause the heat transfer to slow down, but by how much? The Biocab link includes this:

"Does this mean that air temperature would increase by 0.02 °C per second until it reached scorching temperatures? No, it does not, as almost all of the absorbed heat is emitted in the very next second. Thus the temperature anomaly caused by CO2 cannot go up if the heat source does not increase the amount of energy transferred to CO2."

That must be why the air cools quickly when the sun goes behind a cloud. It is the sun that heats up the globe and not CO2. With respect to the forcing of CO2, that site says, "[c]onsidering that the difference between the temperature of the soil and the temperature of the air was 11.5 °C, the amount of 0.15 °C is negligible (just 1.3% of the total)." And for water vapour, "[i]t is evident that water vapor is a much better absorber-emitter of heat than carbon dioxide. Under the same conditions, water vapor transfers 160 times more heat than carbon dioxide.

The above quotes are from this reference:

Nahle, Nasif. Heat Stored by Greenhouse Gases. Biology Cabinet. 27 April 2007. Obtained on 2008/06/03; from http://biocab.org/Heat_Stored.html