Yes, it need to keep the downloaded files, the extracted ones and the old ones at once.You need more space for the installation process than the game will actually take on the hard drive.
The Summerset expansion is ~9gb. Of course if you are getting Morrowind bundled with it that would go larger. Also when I went through the process the game went through an update process on ~53gb? I assumed it was my current game files being patched. How does ZOS handle this process? Do they make a dupilcate folder and run it through that? This I do not know.
Perhaps you need to make sure the directories involved have write permissions.
Just buy a harddrive. If you have a laptop get an external one.
Stupid men are often capable of things the clever would not dare to contemplate...
Terry Pratchett, Feet of Clay
Mines 67.6 GB wtf... It's probably double that when you install..
Also a heads up i'm on Win 7 not Win 10.