The accounts of the destruction of the temple are a little confusing. Jordanes in the 6th century says
“Respa, Veduc and Thuruar, leaders of the Goths, took ship and sailed across the strait of the Hellespont to Asia. There they laid waste many populous cities and set fire to the renowned temple of Diana at Ephesus, which, as we said before, the Amazons built.”
What remained of the temple according to this article
... was quarried by the local inhabitants for its valuable marble and very little is left today. Bits of it have been found in local buildings and Justinian took much of the statuary that survived to his time back to Constantinople.
But according to Cyril of Alexandria in the 5th century, St John Chrysostom was labelled as the "over-thrower of the temple of Diana". Suggesting that he was responsible for the temple's destruction. A similar mention is also given by Proclus of Constantinople who says "In Ephesus, he despoiled the art of Midas". This may allude to the temple of Artemis.
Do we have a definitive answer as to when the temple was destroyed?