From what I have gathered in the casual reading I have done about Late Antique Rome the Temple of Jupiter Optimus Maximus would have likely been closed in the 5th Century. Most Roman temples would have been closed following the Edicts of Theodosius in the late 4th Century. The structure of most temples though, contrary to popular belief would likely have still been recognizable and gold decorations/roof tiles like you mentioned would also still exist in atleast a few temples.

This applies especially to the City of Rome which had a pretty rebellious and conservative pagan elite for quite some time within the Senate. Some of the pagan Senators may have very well spent some of their wealth in maintaining said temples even if they would have been closed and emptied.