I have a student's flute that is letting air out the closed side of the headjoint. I've tightened down the cork with a wrench to compress/widen it but it still is letting some air out. Are there any other tricks? I think I remember seeing some older directors put a cork over a lighter flame, but I'm not sure what they were fixing.
Soak it in water. Cork expands when wet. Once it has expanded, let it sit out until it is dry to the touch. Then put it back in the head joint. I've done this for decades with no issues. In fact, I was taught this trick by a highly respected repairman when I was in college.