Here is what Tim Andersen on Medium says about heat death (and I think he is one of the best science writers I have read): "By 10 quadrillion years, all of the matter in the universe will have decayed into stray photons. Matter as we know it will no longer exist.

The only massive bodies left at this point will be black holes, which decay slowly by releasing Hawking radiation. After about one googol years, ten to the power one hundred, all these black holes will have decayed into nothing.

At this point, the universe will be essentially blank, with little but photons and neutrinos which will redshift to lower and lower energy as the universe continues to expand."

Interesting, this post by Andersen

leaves a strong suggestion of God as creator, but Andersen is careful about any theological claims or statements.

Brian Greene is more definitive about the "nothing" at the end of the universe in Until the End of Time, but I guess they might agree that spacetime remains even if there is nothing to fill it. Not sure about that.