Oh fun.
Yup, we had this happen... the best thing I could come up with was to hit the gum with an ice cube - it should pop right off. If not, whatever remains - run the dryer on LOW heat for about 5 minutes then wipe.
Goo Gone works wonders, too... But you have to clean THAT up before you run the dryer again.
Of course, it depends on WHERE the gum is stuck.
GOOD LUCK!