I would recommend reading/watching Steve Keen's critique of Nordhaus's work (e.g., https://www.youtube.com/watch?v=vwwvZ8g5eHE). Steve Keen is the author of Debunking Economics.
My source: Nordhaus was my thesis advisor in 2016 and I wrote my thesis according to the same critiques Keen raised in this video, and Nordhaus responded to them... this video was from 2019.
If the model described above is not what he actually did, then what is it he did do?
Feel free to link your thesis if its the most succinct answer...
My thesis modeled the tipping points and extrapolated the damage function via monte carlo. Even in worst case scenarios the models didn't return overall damage functions that provoked the dismal theorem. Fundamental solow growth is too resilient (A = innovation). I didn't submit my thesis for publication so it's just in the university archives. Someday i'd like to revisit it with the latest science and another computational implementation and submit to publication.
To be clear, I'm not saying Keen or Weitzman (Keen here is just parroting the late Weitzman) are wrong -- I'm partial to that intuition hence my thesis work. I'm just pointing out that this speech isn't really engaging with the latest literature on the subject meaningfully.
As such I'm unable to tell (with the time I have available here!) how Nordhaus estimates the severity of any given global temperature change i.e. what data is used to calibrate that relationship
And more crucially to tell whether we're measuring the right thing, as all this seems to be measured in terms of consumption which is usually a financial measure: if (repeating my point above) food takes substantially more effort to produce, or is scarce, in a different climate, then consumption could be shown to increase even though people's wellbeing would decrease?
Not OP but here is an example: Steve is famous in Australia for having predicted the collapse of the Australian Housing market in a significant, and (locally) capitalism-ending way. This has obviously not happened.