My thumb swells and shrinks big time.  THE best thing to do is make the thumb hole bigger and use tape.  I bought a work out tool and 220 grit sandpaper.  While bowling, use the tool to make the hole larger and the sand paper makes it smooth.  You want to make the hole large enough to clear when your thumb is at it's biggest.  Well the only way to do this is while bowling.

 I have used the napkin theory and it works but only for one shot at a time.  Plus it shrinks the thumb too much and makes the thumb hole to loose.

Bowling tape works great.  It's so much better to just add some tape of take some out.  You want the perfect fit each time you roll the ball.
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HAMMER NO MERCY is Un-freaking real!  Using this ball is like cheating!

yes i have dont the napkin thing too and i agree with chitown it only works for a short time and it makes the hole too small  

a few months ago at a tournament i got a blister a huge one and i ended ur ripping it off and i think that my thumb may still be trying to build callus because i didnt give it  suffiecient time to heal because i bowl every night and the callus never really hardens could that be  a soulution? Because befor that tournament i never had much trouble with swelling and now i am getting out of the thumb better than ever so i think it may be the callus issue

Ditto on Magic Carpet. A great product that helps reduce thumb swelling.

Drilling a larger thumb hole and using lots of tape is certainly an option, but doesn't work for a lot of bowlers. Personally, I lose too much thumb feel after 2 pieces.

To keep your thumb size down, another option is to get a pre-drilled thumb slug that's the size you want to keep yout thumb at. Especially in longer format tournaments in humid centers, I've found this to be an effective way to keep my thumb at the size I want.

A final solution is to consider using a switch grip system where you can keep 2-3 thumbs drilled at different sizes. I'm using the Turbo Grip system now, and it's very effective.
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"Sometimes, the best move is the one we don't make"

i dont have problem with thumb holes, i drill my balls w/o sleeve slug because i  actually like the feelin of the ball. i had problems long time ago when i didnt have my thumb straight in the hole, later on when i realized that, it was too late, my thumb is a "monsta" now

i have seen many ppl with a tape on the thumb, it works for some of em... i dont think i want to add that
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When a house bowler misses the mark, misses the break point and strike, for many ppl its called a wallshot. When a pro does that its call adjustment

When a house bowler gets his finger stuck in the ball and fall on the lanes, for many ppl its called lame bowler. When a pro does that its called the Machuga flop! ha i like this one.

Before starting practice, wrap a towel once around your thumb and squeeze it at the knuckle.  My thumb swells a lot too, and doing this squeezes some of the blood out of your knuckle which reduces the swelling.  When you get another ball drilled up.  Have them drill it when your thumb is at its "swelling maximum," or get the slug a size or two larger and pop tape in.