Perhaps. I like to think of it as "universes within universes", each forming their own "continuum". Heat death is another matter altogether, I think. Maybe it wouldn't be instantaneous but technically the "outer" universe would experience it much sooner than the black hole itself (owning to the extreme effects of time-dilation near the event horizon). Otherwise it is hard to say when heat death does actually occur, if at all.That universe has experienced a heat death long ago. We are all there is.
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At the moment of creation of a new Universe, the old Universe -- and all other proto-universes -- die an instant heat death and cease to exist.