I don't know -- This all seems to fall into a category of ideas that elicit nothing so much as a "so what?" reaction for me (Like, for example, the simulation argument). Even if this were happening, so what? What can we do with that knowledge?
My main criticism here is that this presupposes that waiting a few billion years for the universe to cool is more efficient than just doing the calculations you want now, at lower efficiency. The "Necessary Assumptions" section proposes Aestivation as a course of action for a civilization expanding "over sizable volumes", which the authors define as interstellar volumes, while still being recognizably the same culture with an ability to coordinate over vast time/space distances. They also propose that this civilization is good enough at eternity engineering to have a shot at waiting out until the universe reaches their desired end state. This, to my admittedly human sensibilities, strikes me as unlikely. Humans definitely couldn't do it without some fairly serious engineering to get us out of our evolutionary intelligence sump (Meaning: We are just intelligent enough for intelligence to cease being a selection factor, as a result, we are locked into our current state until and unless we actually do something about it).
Now, this of course doesn't mean that this is impossible. But it would take beings with a vastly different outlook from us to do it, and that makes the initial assumption (that sufficiently advanced civilizations work to increase their computational capacity at all points) suspect.