@Beskargam:
Sure! Let's start with a basic yet oft-forgotten principle of radiative physics:
Any substance which is a good absorber of some wavelength of radiation is also good at emitting it.The idealized version of this statement is what leads to the concept of a blackbody.
It is often said that CO2 is a good absorber of infrared wavelengths of light, but what is also true is that it is an equally good emitter of those same wavelengths. But if that's the case, then why is it a greenhouse gas at all? The reason is because the atmosphere is not a two-dimensional object; it has depth. Sunlight, peaking in the visible spectrum, penetrates the Earth's atmosphere easily (and thankfully for us), with some of it absorbed by the ground and heating it. The ground then emits radiation back up to space, and by Wein's Law that radiation is longer-wavelength infrared. On its path upward, some of this radiation is absorbed by the greenhouse gases.
Those greenhouse gases aren't just going to hold on to that energy, as we noted that they emit just as easily as they absorb. Some of it get re-radiated back downward, heating the ground further. Some of it also goes upward, and then a portion of that again is absorbed by the layers above it, then getting re-radiated again. You can probably see where this is going: if you treat the atmosphere as being made up of a bunch of thin layers, then the temperature at any layer is determined by how much flux it is absorbing from above and below vs. how much it can freely radiate away. At low altitudes a slice of atmosphere absorbs more from the surface as well as from the layers above, so it is hotter than it would be without greenhouse gases. At high altitudes there is less absorption, but efficient emission since there is a clearer path to space. Therefore the upper atmosphere is cooler than they otherwise be.
The result then is that the presence of greenhouse gases in a planet's atmosphere increases the temperature near the surface and decreases the temperature higher up. There should be some particular altitude where the fluxes balance and the temperature is equal to the equilibrium temperature that you would calculate for the planet if it did not have an atmosphere. (Though clouds and other atmospheric chemistry, e.g. ozone, can complicate this further).
A very nice way to show this observationally is by looking at the strongest greenhouse atmosphere we know of -- Venus. Everyone knows that Venus sports the hottest surface anywhere in the solar system (she's a sexy goddess), despite not being the closest planet to the Sun, because of its dense CO2 atmosphere. But look at the temperature profile:

The upper atmosphere is really cold, in fact about equally as cold as the coldest parts of Earth's atmosphere, despite being closer to the Sun.
Thus by increased greenhouse gas concentrations in the Earth's atmosphere, we should expect to see an altitude-dependent change in temperature; with a warming of the surface and a cooling higher up. Sure enough, this is just what we observe.

Additionally by where the upper atmosphere cools by the same mechanism, that is past where ozone generates heat?
It contributes a cooling effect at the height of the ozone layer as well as altitudes above that. There is also an additional cooling effect at the ozone layer due to reduced ozone concentrations, among other sources, and it is possible to disentangle these effects by examining altitude dependence and relevant chemistry.
Here's a good website for more information. Surprisingly (or perhaps not) the cooling of the upper atmosphere is a topic that does not receive a great deal of study, though there are a few journal articles about it here and there.