As I understand it, there's no suffering in Heaven, and there's nothing up there apart from it. So, as Purgatory is a sort of temporary Hell, it makes sense for it to be down, and not up. The story of Lazarus also seems to imply that the Limbo of the Patriarchs and Hell are close to each other.
We know that Limbo of the Patriarchs is "down" due to the Creed indicating that Our Lord "descendit ad inferos", with inferos being the nether regions.
In the parable about Lazarus, he mentioned a gulf or chasm that seprated those in the "bosom of Abraham" (= paradise, = Limbo Patrum), so that COULD mean that the chasm is the gap between where Heaven is, but not necessarily, where there could have been a chasm between the two.
I don't see Purgatory as temporary Hell at all, but more delayed Heaven, since those in Purgatory are in a state of grace, justification, friendship with God.