Olive,
Your little one finds comfort in sucking her thumb. You will need to find something else, that you can tolerate, that she finds comfort in. Like a blanket, a small pillow, or a doll.
The mitten idea is good and she will grow to dislike it. You will need to tie it on to her hand so that so doesn't get to her thumb. Especially if she sucks at night. This will take a few weeks of rejection and crying but she will get past that and the love for her thumb. Then, of course, you will have to deal with the substitute. Also reward her at the end of the day, then at the end of a week for say 5 or six days of success, with some small treat. (i.e. a piece of her favorite fruit or a jello cup or cookie for a one day treat, and a trip to the library or the zoo for a full week of not sucking. You can use a calander, of hers to keep track of her record.
Good Luck,
mamapri