That is known to be false. Sorry. He just takes past warming and past CO2 and gets one coefficient between them (a slope, in effect). And then current trends in CO2, which he projects forward. Then he imputes a change as large as the CO2 change to the temperature response.
But we know that the CO2 change cannot cause a temperature response that big. It does not produce enough power. Additional power effects equilibrium temperature as the 4th root of the power. Increasing CO2 gives slightly less than linear increases in power (near linear for small changes, but less for large ones as there is some saturation diminishing returns as the sky becomes opaque from below in CO2 frequencies).
The known physical relationship is more CO2 means slightly less than linearly more power, and more power gives a fourth root response in temperature. Instead he just uses linear. The handwaving that this is "simple and empirical" is still hand waving. For a small change you can project the current temperature trend - which is less than this, half. To predict a doubling in the current temperature trend based on the CO2 trend, when we know to a physical certainty the CO2 change cannot cause that big a temperature response, is just the correlation as causation fallacy.
They can't name the power source even for 0.75C in 50 years. 0.4C in 100 years is a more likely figure, from the power sources they can actually name. What we are seeing here is some pressure for realism entering, from the scientific as opposed to the activist side, as it becomes clearer and clearer they have no energy budget to support their scare quote predictions. Meanwhile we get Hollywood nonsense more extreme than the stuff being admitted here to be unfounded.
Hanson has come about half way to reality with this change in his projection. He still has half way more to go.
You should read the linked Scientific American article before reiterating your points. You've always been very confident that you're correct; however, I think that your treatment is simplistic and doesn't take into account a myriad of climate feedback effects, the type of thing that predictive climate models use.
Read the article and then comment.