One other thing is that you may just be using parts of your thumb that you've never really used before. I had the same thing happen to me when I switched from MTB to road and after about a month or so it went away. Also, I feel it when I haven't ridden in a while (after a harsh winter for example).
I'd say fit has some to do with it (however I'd guess that with imporper fit you'd also have some other pains as weell), and you probably do have a death grip, but mainly I'd be willing to bet it'll cure itself with time. Just move your hands around on the bars every few miles to relive the pressure and before you know it the pain will get less and less.