What happens as the Universe nears absolute zero?

At temperatures just abvoe absolute zero, macro scale mass begins to behave in ways we expect only at the submicro scale where quantum mechanics normally rules. What will happen as entropy increases to the point the temperature of the entire Universe is low enough that all mass in it is able to exhibit quantum fluctuations instead of having its sub-atomic particles blurred into classical physical behavior by heat? Is that heat death, or the start of a new phase?