A common error made by skeptics is to go along with the warmist claim that the amount of heat added to the atmosphere by greenhouse gasses can be calculated.

An example is this garbage by David Archibald on Watts UP With That:
The Logarithmic Effect of Carbon Dioxide

Nothing could be more fraudulent than pretending that climatologists can calculate the amount of heat greenhouse gasses add to the atmosphere, as often indicated on skeptical web sites, in addition to the warmist sites. Greenhouse gasses do not add significant heat to the atmosphere.

The temperature of the atmosphere is not determined by the amount of heat entering it nor by the amount of heat leaving it but by an equilibrium between the two which nature establishes and humans cannot comprehend.

There is no mechanism for GHGs to add significant heat to the atmosphere. The temperature of the atmosphere equilibrates with rate of heat loss into space. Almost all heat leaves through the atmosphere, not the surface of the earth. It escapes by going around the GHGs, not through them, as implicit in the results of by Lindzen and Choi. GHGs only block about half of the wavelengths of infrared radiation given off by the earth.

The rate of heat escape is determined totally by the temperature of the atmosphere. Temperature controls intensity of radiation emission. Therefore, temperature of the atmosphere is determined by rate of heat entering and leaving the planet, and nothing can change the resulting temperature of the atmosphere in significant ways.

This means that the temperature of the atmosphere is totally independent of how heat enters the atmosphere. The heat enters the atmosphere a hundred times faster through conduction and convection than through radiation. This is why cooling fans are used in electronics rather than relying upon radiation.

Historical changes in temperature of the atmosphere are due to variations in rates of heat entering and leaving. During an ice age, large amounts of solar energy are reflected off the ice and clouds and into space. To end an ice age, solar heat is captured more easily by increased land mass and reduced cloud cover. None of this has anything to do with the composition of the atmosphere.