I had to do a lot of searching & even called up AOL, just so I could find you an answer.....
Short version: You're out of luck
The AOL software typically places all its temp internet files the same place as Internet Explorer. AOL e-mail is normally either saved on AOL servers (remotely) or on your PC (depending on which setting you setup your AOL).
If saved on the servers, it's gone (for what ever reason).
If on your computer & lost through error.... It's also gone. The file would be encrypted and un-readable. AOL keeps the encryption key (hash) within a small database. If by error it has lost that file... There is going to be no way to recover that file.
HP Pavilion a6750f (tweaked)
Windows 7 Ultimate 64 * Mac OS Snow Leopard