My latest attempt to oversimplify greenhouse gas physics.
On a cold day, we put on a jacket and a hat. They don’t change the amount heat our bodies produce or the balancing amount we release into the atmosphere, but they do make the path for heat to escape more insulating, producing a larger temperature difference between our skin and the atmosphere. The effect of greenhouse gases is very analogous – they don’t change the amount of heat emitted or the temperature at which it is emitted, but they do change the temperature back where the Sun’s heat is being absorbed – at the surface.
In a similar fashion, greenhouse gases insulate the planet. they don't change the amount of heat the planet absorbs from the Sun, and they don’t change the amount of heat the planet radiates. That amount has to balance the energy absorbed from the Sun. They do change the atmosphere's impedance to heat flow, thereby changing the temperature difference between the places where solar energy is absorbed (mainly the surface) and where it is radiated into space (mostly high in the troposphere.)
Because the atmospheric resistance to radiant heat flow (the opacity) has increased, an increase in greenhouse gases causes the effective radiating surface (the average height from which photons escape into space) to move upward. Since the same amount of energy is being emitted, the temperature at the mean radiating height stays approximately the same. Because the Earth’s troposphere cools in a predictable fashion with height (approximately adiabatically), if you increase the mean radiating height but keep the mean radiating temperature the same, the temperature at the surface has to increase. This is the core of the inaccurately named “greenhouse” effect. Maybe it should be called the "warm blanket" effect.