Can you bake a screwdriver?

For example I have to heat up a screwdriver in order to drill it into a lacrosse ball, which is made out of pure rubber. The easiest way to do this would be to heat up the screwdriver. Since I have no other way to sufficiently do this, I was thinking if I could preheat my oven and stick it in their and drill it in the ball while using a oven mitt. Would this work or would it melt the screwdriver's handle to the oven?