The issue you raised before was a bit different: whether actual conservation of total energy was consistent with that dissociation. Any finite temperature above zero, no matter how low, is sufficient to dissociate anything in the limit of low density
, for which an infinite amount of energy is available per particle. However, the time scale would be extraordinarily long since not only is the temperature currently low, but it's dropping as the universe expands. At any rate, I now believe that whole discussion was off-topic, since in a fixed-acceleration picture that's not the path that would be taken toward a flat almost empty universe. In a big-rip picture with growing acceleration it's also irrelevant since the tidal pseudo-forces rip everything apart when they become strong enough.
With regard to the interesting question you raise about QCD, here's a tentative first thought. Remember that this big-rip picture involves an increase in the dark energy density without limit. That includes going past the finite energy density of a quark soup. So I suppose there would indeed be a phase transition as the quarks deconfined, but infinity still beats any finite number.
If some more knowledgeable colleague corrects that, we'll update. Meanwhile, for anyone who stumbled into this discussion I should include a reminder that this big-rip picture is not conventional and has no obvious physical underpinnings. I guess people are exploring it because it's consistent with data on the past acceleration of the universal expansion. The more standard, and more justifiable, picture with a fixed dark energy density is also fully consistent with the data.
(published on 04/09/11)