Yes a bowling ball can sweat with enough heat to the bowling, the ball will start to sweat out the oil that has pick up from bowling. If you place your bowling bag with your bowling balls in the truck of your car during the hot summers months, you will see the oil just come off the oil.
If you take your bowling ball to a pro shop to get clean, they may place your ball in a bowling ball over and they heat the ball up so all the oil can come off. Over time while bowling, your bowling ball will pick up oil and soak it up into the ball.
One of the best ways to get the oil out is with using heat. I would take your bowling ball to a pro shop so they can get the oil out safely. Too much heat can hurt the ball.