To better visualize the absurdity of the runaway greenhouse idea, I did RRTM runs for the tropical atmosphere – with increasing amounts of CO2. That is represented by the blue line below. The red line shows the same experiment with no water vapor in the atmosphere.
The first thing to note is that without water vapor, the Earth would be very cold, no matter how much CO2 there was in the atmosphere. The CO2 runaway greenhouse idea is beyond ludicrous.
The second thing to note is that in the real atmosphere (with water vapor) the effect of even huge increases in CO2 is minimal.
Now here is the real kicker. In the real atmosphere, a doubling of CO2 to 550ppm has almost no effect in the tropics. Downwelling LW radiation only increases by 0.2% from 397.1 to 397.7 w/m^2.