The generated CO2 would have to not blow away to the rest of the planet. The sun shines on the ground in a wide band of the spectrum and heats it up. The hot g

The generated CO2 would have to not blow away to the rest of the planet. The sun shines on the ground in a wide band of the spectrum and heats it up. The hot ground re-radiates mainly in the infrared. The result is equilibrium. CO2 reflects infrared more than the broad spectrum of solar radiation. Thus the ground with CO2 above it still gets heated as much by the sun but the infrared it radiates is partly now reflected back on itself. Thus the equilibrium is altered and the ground gets hotter. So, even if the CO2 didn't spread everywhere, it would still be causing heating locally. The heat would eventually spread everywhere.