If you put this code in the Workbook_BeforeClose() event of the template, it will carry over to each workbook you save with the template. The Save and Save As... options will still work, though. Post back if you don't want those to be allowed (or search the board -- there have been several posts to disable Save and SaveAs.
Private Sub Workbook_BeforeClose(Cancel As Boolean)
ActiveWorkbook.SaveAs Format(Date, "mmddyyyy")
Hope that helps!
How to use the above code:
Press Alt-F11 to open the VBE.
Press Control-R to open the Project Explorer.
Click "Microsoft Excel Objects" for the file you're working on.
Double-click the ThisWorkbook module.
Open the Code pane with F7.
Paste the above code in.
Press Alt-Q to close the VBE and return to Excel