My daughter is almost 5 and has been a major thumbsucker since she was an infant. Her pediatrician tells me not to worry about it because everything is correctable and he went through the same challenges himself with 4 of his own kids. My dentist on the other hand has a fit everytime he sees my DD because you can already see the changes in her jaw structure because of it. He said the only positive is that she doesn't have a thumb preference so the changes are balanced.
I was a thumbsucker myself and I have memories of my parents trying to get me to quit, so I know the challenges they present. Anyway, I decided to address it with my daughter, but in a low stress, she needs to take the initiative way. This is what I have and am continuing to do:
First, I said she can only suck her thumb in bed. Whenever I caught her sucking her thumb I told her she needed to go to bed. She would often choose to go to bed and I would find her in her bed on her own just so she could suck her thumb. If I would remind her about sucking her thumb, she'd get mad and say, "I WANT to suck my thumb." I never made a big deal out of it and tried to give her the power to choose.
I also learned that when I caught her sucking her thumb it was often because she was tired/bored. Frequently, I would have to make the effort to engage her in an activity...play a board game, dance, etc.
We tried painting her nails and wearing bandaids on her thumbs (at her request), but then she said it wasn't worth it because she'd just suck her thumb anyways.
I took my DD to Toy's R Us and offered to buy her any baby doll she wanted (she LOVES dolls) if she stopped sucking her thumb for a month. She was excited and motivated, but that time frame was too much. What has finally worked is that I started doing smaller time frames and rewards.
I told her that if she stopped sucking her thumb for a week I would take her to a ceramic painting shop she enjoys and she could paint whatever she wants (it helps I had a coupon!). I told her she could have 3 warnings for the whole week. She needed all 3 warnings, but she did it! The second week I told her I would take her to pick out her own Easter dress. Again, I gave her 3 warnings. She only needed 2. We bought her a beautiful Easter dress, something I would've bought anyway, but she got to pick it out!
I have not told her about another reward since and she has reminded me about the baby doll. So, I told her that if she is thumb free for a month we'll go buy her a baby doll. I have yet to see her suck her thumb once. She's not even sucking it in bed!!!
I'm optimistic, but not holding my breath. My daughter is very stubborn, but this is the process that is working for us. Every child is different. I hope you find something that works for you! Good luck!