This started several months ago. Word started saving these files, and they
are really piling up. I looked at the Options in Word and couldn't figure
out whether any of them had anything to do with the problem. I am afraid to
delete the files because I am not sure if that information is needed by Word
at this point.
Did you ever get a crash (of either Word or Windows/the computer
itself) while you were working in Word? That seems to be when the temp
files don't go away. When you reopen a document after a crash, Word
offers you a recovered version, which often contains more of what
you've done than the most recently saved version; once you choose
which of the versions to keep and which to ignore, you don't have to
worry about the temp files.
If you have the folder open on your desktop in which your document
lives while you work on it, you can see the buildup of temp files, and
when you close your document/quit Word, if you look quickly you can
actually see the temp files disappear.
The Disk Cleanup utility (in Windows) claims to get rid of unneeded
temp files, though it doesn't seem to do it thoroughly. You can Search
(in Windows) for all files on your computer with ~$*.*.tmp (I think
I'm remembering it correctly -- it was posted here a week or so ago in
answer to a similar question) -- not sure why you need two stars --
and then Delete them when Search is finished. (Turned out I had almost
1000 such files parked in odd places, some of them several Mb.)