Recovering overwritten word file

You could try recuva: http://www.piriform.com/recuva

If you did a Save As over the top, then I think your options are really limited.  If the file was Deleted instead, it's much easier.  

Depends a bit whether it is on a local hard disk or network location.

Recuva is pretty easy to use:
http://www.piriform.com/recuva

The next level up is something like GetDataBack - free to *test*, but it won't actually recover till you pay.  Saved me on at least 3 occassions so far.
http://www.runtime.org/data-recovery-software.htm
 - you probably need the NTFS version.

It was actually overwritten by a different file with the same name, not saved on top.

Chances of recovery - poor
You could try a third party utility but I'm not optomistic - if you do use a third party tool DON NOT INSTALL IT ON THE SAME DISK otherwise it may also overwrite the document - you may have to remove the disk and slave it in another machine it its your only disk

Lots of tools tyou couls try - recova has been mentioned - here is another http://www.officerecovery.com/freeundelete/

With the word document open, see whether the link below can help you.

http://www.nirmaltv.com/2009/07/22/how-to-manage-document-versions-in-word-2010/

Possible alternate is if the *.tmp file is located I'm the same directory as the save file.  It usually stays if you had word crash but sometimes it stays any way.  You would simply change or add the extension or .doc or .docx.