B.,
I have had a lot of luck with "trading cozys". When it was my daughter's time to ditch the paci, we had started to call it her cozy. She got to pick out something form the store that could be her "new cozy." One time, it was a blanket, another time, it was a teddy bear.
I realize with it being her thumb, you cannot take that away. That, of course, it the hard part here. When my daughter came home from daycare with her thumb in her mouth, I told her that she was to take her paci back, because I knew it would be nearly impossible to take the thumb away, so I got lucky there.
Sounds like she is orally fixated, and needs an oral soother. Maybe she could go tot a paci, then trade in her cozy, in a few months, just to rid the thumb habbit. The worst thing about it being her thumb is the fact that it is very damaging to her teeth, and perhaps speech from there.
The paci transition might be very difficult, because it is not the thumb, and doesn't have to warm fleshy qualities that the thumb does, so you will have to make the paci more enticing. You can dip it in honey, or condensed milk...whatever she might be into...sprinkles even. (if you do this, remember to brush more so the sugary stuff gets off of her teeth instead of causeing dacay) Sounds crazy, but reward her for keeping it in during a half hour tv show....anything to get her used to the soothing of something other than her thumb. I know a lot of people might thing I am crazy to encourage these things, but they might not realize the difficulity of taking the thumb away.
Good luck to you and yours!
A.