birdtray binary package in Ubuntu Mantic amd64

 Birdtray provides systray notifications for Thunderbird. It displays the
 count of unread mail, hides the Thunderbird window when not in use, and
 restores it on clicking the tray icon. It also provides a context menu
 with commands such as starting composing a new mail.
 .
 It is a nasty hack -- an external process looking at Thunderbird's
 insides, it suffers from problems like noticing new mails only after a
 delay, having to restart Thunderbird just to hide its window, etc --
 you'd want to use an extension like firetray instead -- but, it is
 likely that support for Thunderbird XUL extensions will be dropped soon,
 possibly by the time you read these words.

Source package