I don't know the answer; I would guess it would be approximately linear over the range of conditions we are likely to see, but nonlinear over a larger range. Would some boundary conditions may be useful here, perhaps the range between a snowball earth and an ice free earth?
Interesting question, worthy of a star; hopefully you'll get some sensible answers.
Edit; regarding your analogy: If you plug in a heater, the room would warm quickly at first, then the rate of warming would slow as the new equilibrium temperature was approached. But if the room was 70% aquarium, then after an initial warming the rate would slow more rapidly as more heat is absorbed into the aquarium. Although the equilibrium temperature would be the same, it would take much longer to reach since the water would act as a heat sink until it too reached equilibrium.
However, for the room at 150F, the heater wouldn't be able to raise the temperature to 170F since the warmer room would lose heat more quickly. Indeed, I think the heater would struggle to get to 151F let alone 170F. (assuming that the room would behave approximately as a black body radiator)
I don't think humidity would make any difference in a room since it would be the walls that radiate the heat away (unlike the Earth where some of the heat is radiated from the atmosphere)
But is a room with a heater a good analogy? After all, the heat in (from the sun) is the same (or nearly so); it is the ability of the planet to lose this heat which is changing. Perhaps a room lined with thin layers of an insulating material would be better. You could say that doubling the insulation would increase the room temperature by 1 degree. But what if the initial conditions were different? well my guess; and I stress that this IS a guess, would be that the increase due to the insulation would be proportional to the uninsulated temperature (measured from absolute zero) I don't think it would be constant.
Of course, this doesn't really answer your question about climate sensitivity, which is about the feedback response; I would expect that the Ice albedo feedback would vary in strength for different temperatures. (which is why I suggested the boundary conditions above; either side of these extremes, this feedback wouldn't be there and climate sensitivity would be less) I can't think of any more though; perhaps others can do better.
It probably is. For it not to be would be a case of linearity which is rare in science.
In particular, in a world much warmer than what we have now, there would be no ice. As a result, there would be no feedback due to changes of albedo due to expansion or melting of ice. Climate sensitivity would be lower in such a world than it is in the present world.
It would depend on the heater, and also on the room's suroundings. Is the room a hut at the South Pole or is it in a large building which is the same temperature as the initial state of the room.
I think for political purposes it is important to get out a number and that number has to be big enough to be at least somewhat alarming. It is also important to make sure that number is hard and fast. IMO, there is very little reason to believe CO2 is the dominant driver of temperature as alarmists would like us to believe. Other factors seem to play a far more dominant of a role. When those factors are variable, and the climate sensitivity is small (and possibly variable) it is lost in the noise.
I don't know and I am pretty sure, nobody knows for certain, but I expect that climate sensitivity would reduce as temperatures rise, if only because the temperature of space is constant, and an increase in earths temperature would increase the out going radiation, and I am sure there are other negative feedbacks as well, good question.
The planet is constantly battling to stay warm. Whether the average temperature is 53 F or 55 F is irrelevant. The question is if CO2 will cause a "runaway effect" and burn up the Planet? That question was answered years ago, yet the alarmists are still "pounding the pavement" and still screaming about it.
Your analogy has the exact premise of AGW activists.
When we read about climate sensitivity, we read about a fixed number with some range of uncertainty. And we also know that there are many studies which come up with different values using different methods or different time periods, etc.
But If you think about it, why would a doubling of CO2 result in some fixed amount of warming for all initial conditions? (Any scientific discussion of this would be great.)
