USB cord caught on fire while charging. Headphones toasted?

I think I learned a lesson the other day: Do not charge Beats headphones in the car. We took a 20 hour drive, and while I was not driving, I listened to the XM radio via my Beats Studio Headphones. When they needed to be charged, I plugged them into a car adapter. Then I picked up the headphones to move them, and the cord was ON FIRE!!

Literally burning, with flames coming from the cord.

Now, the headphones seem to have been toasted as well. They won't turn on or charge anymore.

Has anyone experienced something similar, and if so, were you able to repair the headphones? Or did you have to throw them out?

Thanks!