Every few minutes, Word seems to save something by itself; I see the readout flicker across the status bar. But I know it's not saving my document, because the document still contains unsaved changes.
What you're seeing is Word's AutoRecover feature automatically saving a backup version of the document in case Word, Windows, or your computer crashes. When you restart Word after a crash, it automatically opens the latest AutoRecover documents so that you can choose which to recover (see the previous Annoyance, "Recover a Document After a Crash"). If you close a document normally, Word deletes its AutoRecover document.
If you've lost work in Word documents to crashes, chances are you now save the active document whenever you've made any changes to it that you want to keep. (Yes, I too obsessively press Ctrl+S at the end of each burst of typing.) In this case, AutoRecover offers little benefit. To turn it off, choose Tools » Options, click the Save tab, and uncheck the "Save AutoRecover info every" box.
If you tend to forget to save your documents, make sure the "Save AutoRecover info every" box is checked and set a suitable length of time in the Minutes drop-down list. The default is 10 minutes, which is fine if you're poking at a document. If you're typing 100 words per minute, shorten the interval and check "Allow background saves" so that you can keep working through most of the AutoRecover process. (Of course, you're better off saving your documents more frequently.)
Word saves AutoRecover documents using the name AutoRecovery save of <document's name>.asd. For example, the AutoRecover document for a file called Benefits statement.doc would be named AutoRecovery save of Benefits statement.asd. Word saves AutoRecover documents in the folder specified in the "AutoRecover files" line of the File Locations tab of the Options dialog box (Tools » Options). The default location for Word 2003 is your %userprofile%\Application Data\Microsoft\Word folder.
UNDERSTANDING TEMPORARY FILES
The temporary files you're most likely to notice are those that Word keeps in the same folder as the document itself. These contain versions of your document that you have saved earlier in the current editing session. When you close the document normally, Word deletes the document's temporary files. In a long editing session, the temporary files can stack up, and Word may take several seconds to delete them. This is why Word sometimes seems to take a surprisingly long time to close a document that you've already saved.
The temporary files you're next most likely to notice are the owner files that Word uses to lock the documents you (or other users) open. When someone opens a document, Word creates an owner file, giving it a name consisting of the document's name with the first two characters replaced by ~$. For example, for a document named Second Thesis.doc, Word creates the owner file ~$cond Thesis.doc. (Very short document names receive a different treatment.) When you try to open a document, Word checks for the existence of an owner file, which would mean that someone else currently has the document open. Word deletes the owner file when the document is closed. Owner files won't trouble you when Word is running properly, but if Word crashes, these files may be left undeleted. If this happens, you may need to delete them manually to restore normal behavior.
Word creates several other kinds of temporary files, including a temporary file that it creates at startup to enable you to use OLE (Automation) objects in your documents. You're unlikely to need to work with these other temporary files, except to delete them en masse after Word has crashed.