We'll take an example of Venus as a poster child for runaway greenhouse effect.
First of all, let's talk of day/night changes. At the surface level there is little to no change as Venus has an albedo of 0.77, i.e. its atmosphere reflects back 77% of light. Compare this to Earth's albedo of 0.3. So in the overall energy balance of Venusian atmosphere the amount of heat coming from the Sun plays a rather small role and most of it will affect only the upper layers of the atmosphere.
And even what light is not immediately reflected back is mostly absorbed by the atmosphere and as a result the day/night temperature changes are practically nonexistent. The lower atmosphere has approximately the same temperature during day or night, at the equator or at the pole.
At the same time, like most of terrestrial planets Venus continues to produce heat primarily as a result of decay of radioactive elements in the mantle. This heat replaces the amount that is lost from the atmosphere into space.
What results is a stable system and really the only thing that can affect it at this stage is the gradual reduction of the nuclear decay heat over time.
Having a very long discussion in the comments so I figured I'll update the post to better explain what I meant in the post.
A planet's atmosphere is a thermodynamic system that in the case of Venus appears to be in the state of equilibrium, i.e. heat received in the system equals heat lost to space primarily via IR radiation.
The main parts of planetary energy balance are as follows: incoming solar radiation and geothermal heat as sources of income and loss is primarily radiative.
Geothermal heat also consists of residual heat left over from planet's formation and additional heat generated by the decay of radionuclides. In the case of the Earth geothermal heat is estimated at some 47 TW about half of which is estimated to come from the residual heat and half - from radioactive decay. I couldn't find any reliable sources for Venus, but due to similarities in composition it's reasonable to say that it would exhibit similar energy flux but due to lover volume it's likely to be around 40 TW.
So now the overall simplistic view at the components that result in constant atmospheric temperature of Venus:
- Albedo of 0.77 limits the amount of solar radiation from an initial flux of $\approx 2601 W/m^2$ to only about $157 W/m^2$ enter link description here
- Additional minor energy income comes from planet's interior as discussed above.
- Finally, heat escapes primarily via IR radiation.
- High density of atmosphere distributes energy more evenly.