There are many different empirical results that lead to current consensus of climate sensitivity. The consensus is the consequence of these. A good summary is at http://www.skepticalscience.com/climate-sensitivity-advanced... in figure 4.

> And Plass definitely missed at least one non-linearity.

AFAIK he only included CO2 and water vapor (as a feedback) in his calculations. There are many more both positive and negative feedbacks, such as methane or aerosols. But they pretty much cancel out in the end, as more complex models indicate. And Plass was completely ignorant of climate history, which is also one of the important sources of climate sensitivity estimates.