No, I'm just remembering what my Astrophysics teacher taught us so I'm not sure what this "Big Freeze" is. Space is supposed to be at 0K since it expands, it doesn't move. But it's near 3K. Which led scientists to believe that the 3K background radiation is the remnants from the Big Bang when it was still a singularity of infinite energy. Though I was thinking about more and I'm unsure if that radiation will dissipate or not and the 3K might be a result of the universe thinning it out as it expands. Thus it thinned out to 3K and should settle to an near 0 level but not at it. Not sure what would be true, I'd have to ask a physicist on what would happen to the radiation.
From what I understand space will approach absolute zero but never truly achieve it nor will absolute zero be possible so long as it can be observed. Observing something influences it at the quantum level which makes it impossible to measure an absolute zero state. Space is not empty. It has quantum makeup just like anything else. The only way absolute zero is truly possible is for everything in the universe to be in that state so that no observations can be made and thus no quantum excitements can occur.
This is assuming that things at the quantum level can also be put to a halt which, from our current understanding, they actually cannot. Things that happen on a macro scale often mean jack to things on the quantum scale but things on the quantum scale can quite easily influence those on a macro scale. As long as something is happening at those tiny scales absolute zero cannot truly be achieved which means it never will be, based on our current understanding, since things at the quantum level often do as they dang well please regardless of what even common sense would tell you.
The Big Freeze is the growing scientific consensus on the ultimate fate of a lone universe in which the expanding distances of matter, lack of gas to form new stars, and increasing number of black holes eventually lead to an entire universe at near absolute zero which is incapable of sustaining life as we know it. A state of maximum entropy is then reached where information can no longer be processed. Basically, everything becomes freezing fudgy cold to the point where everything dies and then eventually nothing can happen at all. The good news is that quantum activity will still likely, at some point, give rise to a type of big bang which would start a whole new process.