In Word 97 thru 2003, AutoText entries are stored in normal.dot unless you specifically choose to store them in other templates.
AutoText in 2007 is also known as Building Blocks. Be aware that the AutoComplete tip box no longer appears in 2007 except for dates and you need to insert entries with F3 as Enter no longer works. Otherwise, you have to drill down several menus to select individual entries.
There are a couple of ways you can transfer your entries, but the easiest may be to place your old normal.dot in Word's Startup folder. You'll want to strip other customizations from the file that may conflict with the new normal.dotm and change the name of the file to something like myautotext.dot.
It's getting more and more difficult to transfer AutoCorrect and AutoText between Word versions. It may be time to consider a true text expander that will work in all programs, not just Word. :)