Goodbye swaddle

Yesterday morning, I went into Jack's room to find him completely out of his Swaddle-Me - it was bunched up next to him. Time to move on...now he sleeps in a sleep sack! (And did great with the change.) The only problem is that his hands are cold in the morning - I'm not sure what to do about that, since he also sucks his hands ALL THE TIME now. So I don't really want to put mittens on, because they'll just be wet and cold then. Any ideas?