Apple - Where does Quicktime store its screen recordings?

As of OSX Sierra, it's here:

~/Library/Containers/com.apple.QuickTimePlayerX/Data/Library/Autosave Information

In there, there is a container/package/directory called Unsaved QuickTime Player Document.qtpxcomposition that contains a Screen Recording.mov file with the actual video. You can copy-paste that mov file wherever to save it permanently.

You can also double-click the Unsaved QuickTime Player Document file directly. That file opens in QuickTime, and allows you to save in a proper place. Note that sometimes QuickTime will fail to save a Screen Recording with the error "The operation could not be completed" (using File > Export As might work, though), so copy-pasting is probably less prone to error.

My battery ran out when I was recording and found my file there.

Although the recording did stop when closing the lid, it does not mean that the recording is saved.

If it is, by Command clicking on the file's name, the full path where you can find it will be displayed.

The default storing place, of course, is under ~/Documents.