As the universe expands, ultimately, will it continue to reach closer and closer, to absolute zero but never get there?

Question

First law of thermodynamics, the conservation of energy, doesn't this law all but guarantee that regardless of how far the universe expands it will forever contain its original amount of energy? All the matter in the universe will break down and all the energy will reach an equilibrium. However, because of the conservation of energy, the universe will never reach absolute zero will it? As it expands, the universe will continually get closer and closer to absolute zero, but it will never completely get there, or will it? How many billion years will the universe be between 1.0 degrees Kelvin and .01 degrees Kelvin. Is their a mathematical formula that describes the cooling rate of the universe towards absolute zero, once the universe has reached thermal equilibrium?

Mr Anderson · Answer

In the dark-energy-only far future, the Universe will asymptote to the de Sitter temperature, the minimum temperature possible in the Universe, which is NOT absolute zero (absolute zero is un-physical, the 3rd law of thermodynamics needs an update). In natural units:
$T_ds=1/2πl$
Where $l$ is the radius of the future cosmic event horizon.

As the universe expands, ultimately, will it continue to reach closer and closer, to absolute zero but never get there?

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