On Wattsup this got illustrated with our core body temperature. That stays constant even when the forcing is changed.
Now while there is somewhat limited evidence in my opinion for the climate being like a thermostat, there's also precious little against it. We just know too little about world albedo and relative moisture content. We cannot measure these terribly well now and have a very poor grasp of past changes.
These factors are quite capable of completely counteracting CO2. We do not have a billion Earths, where we could pick 2000 for controlled experiments with statistics derived from 1000 runs on Earth without anthropgenic effects and 1000 with them included.
But let me do a thought experiment. In that thought experiment, we leave out CO2 changes and everything else constant and a physically possible result would be that the temperature change is identical up to date.
While I consider the notion that a climate thermostat is unphysical a myth, there's another myth shared by both sides of the debate.
The 0.8C or thereabouts increase is supposed to be much smaller than it would be based on the forcing, because much of the increase is temporarily hidden by aerosols and ocean warming.
Now suppose, the aerosols did in truth cancel out in their effect and there was no ocean warming, it's blithely assumed that this would continue to be the case in the future.
It's quite possible that clouds or the ocean surface through albedo changes keep temperatures down now, but there is no guarantee they would in the future. In fact, all thermostats break given enough being thrown at them.
I like another example of a thermostat, a petrol tank open to the atmosphere. It'll resist the forcing through evaporative cooling; at some stage though, it stops acting like a thermostat and there is an explosion.

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