I know the Gift of Men was to leave the circles of this world, but does Tolkien ever discuss the further fate of Men? Does he talk about Heaven, Hell or Purgatory?

I remember allusions to these concepts in the fate of the Elves, and how they may be kept in the Halls of Mandos for longer or shorter periods before possibly taking up their lives again in Valinor (and maybe even returning to the East). Is there a similar discussion/explanation for the fate of Men?