I have a Thawing Glaciers, a Thespian's Stage, and Deserted Temple on the battlefield in addition to four other mana producing lands. In the previous turn I tapped Thespian's Stage to make it a copy of Thawing Glaciers.
I tap the Thespian's Stage (Thawing Glaciers Copy) to search my library for a basic land.
I then use Deserted Temple to untap Thespian's Stage
Finally, I use Thespian Stage's copy ability to copy the basic land that just entered the battlefield.
When I end my turn and enter the cleanup step, the text from Thawing Glacier's ability attempts to take effect, "Return Thawing Glaciers to its owner's hand at the beginning of the next cleanup step"
Does my Thespian's stage get returned to my hand, or does nothing happen because the card that activated the ability is no longer a Thawing Glaciers?