Good that you've read it, but I'm afraid the entire idea of this analysis just seems absurd to me. It's exactly the kind of thing that creates the replication crisis, which outside of the experimental sciences is driven by a morass of P=0.049 modeling claims that disappear when re-examined. Many such papers are well cited, are claimed to use "robust" methods and so on. Yet when the claims fail to generalize, nothing happens. There's no postmortem or other institutional attempt to learn anything, no period of self reflection or adjustment of methods. Academia unfortunately no longer has credibility when it comes to this type of statistical analysis.

Maybe they address all of these obvious problems in their paper, but I doubt it:

1. The low quality and wide CIs of the temperature datasets themselves. Look at the recent revelations about the CIs on the UK's weather data for an example (and the total lack of care from the Met Office about fixing the situation). It's one country but similar problems are found everywhere. One of the most depressing conclusions I reached when studying this topic a few years ago was that we don't really know if the world is getting warmer or not. It's not even a well posed question to begin with, and the datasets are subject to massive historical revisions, but even ignoring those fatal problems the error bars on the underlying data are wider than the claimed increases.

2. Dubious nature of the gridded GDP dataset they're using. Much of the data comes from sources merely cited as "literature". Of those, many are themselves estimated and modeled data dubious on their face, e.g. the Australia data comes from a paper with only two citations (one of which is this paper) and which claims to accurately reconstruct GDP back to the 1850s! This is a jenga tower of estimates and there doesn't seem to be any attempt to measure or think about error in a systematic way: they explain that they looked for outliers in the data to do manual validation (unmentioned, did they remove outliers?), and they admit that the dataset has serious problems, but just blithely hand wave it all away. There is no attempt to estimate the accuracy of their data beyond observing it isn't 100% accurate.

3. Inability to validate the resulting model ("robustness tests" aren't the same thing as validation, at all). Unvalidated models aren't useful for anything.

As for Nordhaus, I wouldn't try to outsource decisions about the reliability of work to old names. They've been pointing out serious problems in the literature for years, some of them decades, and there have never been reforms. If someone warns of problems 100 times and is ignored every time, the lack of a warning the 101st time doesn't mean anything. They could just be tired. I would be, in their shoes!