Why CO2 and downwelling radiation is not against the laws of thermodynamics

There is a common misconception that CO2 doesn't radiate back to earth, because it is against the law that no cooler body can heat up a warmern body. So I was forced to write a short explanation on wattsupwiththat.com
 https://wattsupwiththat.com/2017/01/10/the-william-happer-interview/

My reply was to this comment:
https://wattsupwiththat.com/2017/01/10/the-william-happer-interview/#comment-2393740

"Great post, but why would CO2 cause any warming at all? Unless you agree with the GHE theory, which I doubt, this claim of “only 1C warming” is not valid within the laws of thermodynamics."

This "CO2-warming-is-against-laws-of-thermodynamics meme" does a great harm to the skeptics reputation, because it ignores simple radiation physics.

Just to get the idea:

• There is a stove in a cold room, giving out a certain radiation energy.
• Now take a black matte painted solid sheet around in a certain distance from the stove. It will be heated up and radiate towards to stove and the rest of the room. The stove will be hotter to a certain extend. This is what a cloud does, being close to the properties of  ab blackbody.
• Now take away the solid sheet and put there a black matte one with holes punched in, so that about two thirds of the area is covered. So this is now also heated by the stove, but to a lesser extend, and also the stove gets a little hotter. This is what watervapour is doing, leaving through some radiation.
• Now take another black sheet with lots of holes punched in, covering only one quarter of the area. Now the re-radiation is much lower, and the stove stays only a small amount hotter. This is what CO2 is doing in the atmosphere.
• Now try to get the whole picture: CO2 is always there in a quite even distribution. This is the sheet with the big holes. Water vapour is not evenly distributed, So it compares to a second sheet behind it,with differently big holes. Clouds are not always there, but if, they are covering the certian area completely.
• We see: CO2 has a small function in the radiative play. So it doesn't really matter that much.
• But: All three components of the atmosphere are re-radiating some amount of heat, thus slowing the cooling of the "stove". They are cooler than the stove and they are not heating up the stove. There is always a net flow of heat towards the cold room. Sometimes more, sometimes less, and always within the laws of thermodynamics.