The temperature profile of planetary atmospheres is controlled by insolation from the central star and by the radiative transfer properties of their gaseous components. We assume a chemically-unspecified planetary model-atmosphere, whose absorption properties are approximated by a semi-grey model step function. We investigate the response of the atmospheric temperature profile, especially the ground temperature, to changes in the model-atmosphere’s radiative transfer properties, by introducing a concentration change of a general model Green-House Gas (GHG), having different absorption properties in the near- and far-IR spectral regions. The molecular absorption is parametrized by three parameters: The wavelength of the step function resulting from the semi-grey approximation, λ_cut, and the two absorptions: κ_vis ≡ κ(λ < λ_cut) and κ_FIR ≡ κ(λ > λ_cut). We also define the plane log(τ_vis); log(τ_FIR), where the contribution of both values makes up the total optical depth, according to the semi-grey approximation, in the shorter and longer wavelength regions, respectively. Each point in the plane represents a model atmosphere, and results in a calculated ground temperature T_grd, which is represented by the vertical axis. Although the ground temperature is obtained independently of the specific atmospheric chemical composition, an average absorption calculation of a real atmosphere may be corresponded to our model. We identify three domains in the above ground temperature dependence on log(τ_vis) and log(τ_FIR): domain A, in which any increase in concentration of a GHG leads to higher T_grd and a hotter atmosphere. Domain C, in which any increase in concentration of a GHG leads to a lower T_grd and a cooler atmosphere, and domain B, where changes in the amount of the GHG may cause either heating or cooling. All three cases appear in the solar system. The connection to habitability will be discussed, time permitted.