I try to find the relevance in this;
”Now, consider rerunning the simulation, but with a slightly different longwavelength cloud forcing. Again, if we run it long enough, it will settle to an equilibrium state, in which the fluxes balance, and the temperature is constant. However, since the longwavelength cloud forcing is different, some of the other fluxes will also be different, and the equilibrium temperature will, consequently, also be different. There will be an offset, compared to the first simulation, but it won’t grow with time simply because one simulation had a different longwavelength cloud forcing compared to the other”


I cannot find this offset in the heat transfer equations. But there is a time-dependent drop in temperature from dropping the emissive power of a heat absorber, like what happens when increasing the amount co2. It shows that without increasing the power of the heat source, the only effect is dropping temperature of the system.