Technically, Chromium downloads the file to the Cache directory (defaults to
%userprofile%\Local Settings\Application Data\…\Cache), and then moves it to wherever you choose to save it.
What you could try is to leave the Save As dialog open until the transfer ends instead of clicking Save. Then you could run the file directly from your Cache directory (which is easy to clear), except that it will be unnamed so you’d have to find it—which isn’t really that hard since it will be the most recent file.
A better (and probably the currently easiest) solution is to simply have it auto-open .torrent files. Download one, then click the down-arrow of the file in the download bar and select Always open files of this type. That way, when you get the Save As dialog, you can just perpend
%temp%\ to the filename, and click Save. Then it would open the .torrent file and would be erased the next time you clear out your TEMP directory.