walking a heapq nondestructively without duplicating?

[Tim Chase]

I've got a large heapq'ified list and want to walk it in-order
without altering it.  I get the "unsorted" heap'ish results if I just
do

  from heapq import heappush, heappop, nlargest, nsmallest
  my_heap = []
  for thing in lots_of_items():
    heappush(thing)
  for item in my_heap:
    ...

To get them in-order, I can do something like

  while my_heap:
    item = heappop(my_heap)
    do_something(item)

to iterate over the items in order, but that destroys the original
heap. I can also do

  for item in nlargest(len(my_heap), my_heap): # or nsmallest()
    do_something(item)

but this duplicates a potentially large list according to my
reading of the description for nlargest/nsmallest[1].  Is there a
handy way to non-destructively walk the heap (either in-order or
reversed) without duplicating its contents?

-tkc

[1] http://docs.python.org/2/library/heapq.html#heapq.nlargest