"how the heck do they measure that so accurately from so far away anyway?"
They don't. From the paper:
"Current technology simply does not allow us, for example, to measure global temperatures on extrasolar planets anywhere close to the accuracy needed."
The temperatures are actually little more than guesses based on several entirely unsupported assumptions about what the planets might possibly be like. For example, the one quoted as having the "most Earth-like temperature" comes from this paper https://doi.org/10.1051/0004-6361/201936929 which says:
"We find that the stellar radiative energy flux of the new transit candidate would be times the insolation atthe top of the Earth’s atmosphere. An Earth-like Bond albedo of 0.3 would result in a globally averaged surface temperature of about K... hese calculations neglect the additional heating of the greenhouse effect, for instance, from water vapor (H2 O), carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), ozone (O3), and other greenhouse gases. On Earth, the greenhouse effect amounts to about + 33 °C. If the transit candidate signal belongs to a genuine planet and if this planet has an atmosphere that provides an Earth-like greenhouse effect, then the globally averaged surface temperature is around + 5 °C."
In other words, if the surface is very similar to Earth's, and if the atmosphere is very similar to Earth's, and if the radiation received from its star has been calculated correctly, and if there's actually a planet there at all, then the temperature will fall somewhere in the estimated range. The actual detection method used, looking at variation in the star's brightness due to possible transiting planets, cannot provide any of this information, it's all pure guesswork about what things could be like given the best possible assumptions for life. Which is why it's a very minor part of that paper, it's actually about the detection of the planets and speculation about their possible properties is just a small side note.
As for the original paper, the headline of this article is extremely misleading. Astroboffins haven't spotted anything. The paper is simply an analysis of already known planets, trying to assess their potential for habitability using criteria decided by the authors. It doesn't add any new information, it's really just saying something along the lines of "Here's a way of looking at the information we already have in a way that might be interesting, and here's the additional information we would need in order for it to actually be useful". There's no new discovery, or even anything particularly interesting going on, just some ideas about what we might like to know once we have better technology and techniques for looking at things.