The Earth would cool while the atmosphere near the Earth would warm some. But that is a gross over simplification. What I have been attempting to convey is that the extent of warming of the lower atmosphere might be quite negligible, depending on the concentration and distribution of green house gas, and of course its absorption characteristics. It is not enough to say this or that gas is a greenhouse gas. Also, It would not be possible to eliminate the cooling contribution of vertical convection driven by density difference between the surface and the upper atmosphere. When you have, for example, other much more important temperature moderating components of the atmosphere, the contribution of such a weak greenhouse gas as CO2, at a very small concentration, may be negligible. My best guess, it is only that, is that we need CO2 to maintain plant life, without which all animal life would parish, but it is an incidental and unimportant direct contributor to global temperature moderation. I could be wrong but our best and most recent data suggests to me that my guess is probably close to the actual situation.
I think you may have missed my main point which was that if Hansen's hypothesis depends on there being positive feedback to the effect of elevating CO2 than Hansen's hypothesis is wrong. And importantly everything dependent on Hansen's hypothesis being right is therefore also wrong.
Would you at least agree with that?