Google working on improved download handling in Chrome
Change is on the way, however. In the Chromium design docs, there's talk of building robust temporary download handling in to Google Chrome. As the doc describes it, the change would "provide a nonintrusive way to open downloaded files with another application without permanently storing them on disk." An addition would be made to Chrome's context menu allowing you to "download and open" a file -- like a .torrent -- without having to save it first.
Files downloaded that way would still appear on your shelf (the chrome://downloads page), but they'd be marked with an icon indicating their unsaved status. You can work with your "download and open" files as you would a normal download -- but Chrome would remind you that you have unsaved temporary files when you close the browser in case you want to save them permanently.
Reduced file system clutter like mine is one benefit, but it would also be advantageous for Chrome's Incognito mode. Sign into your email, open and print your docs, and close Chrome -- when you confirm the prompt, the temporary files would be purged.
So, when can you expect to see the changes? Don't hold your breath -- this is actually related to a Chromium bug filed back in September of 2008.