Had to change a belt in the middle of our trip when we were in New Orleans. It had been squeaking since San Antonio and I couldn't stand it anymore. I always carry a extra but unless it were to break like yours did it stays under the seat.
Your belt, being 8 years old, regardless of mileage is due to be changed. It had probably been degrading for a while and depending on the recent repair Toyota did they may have never even looked at it.
How did the motor overheat? Did not all the red warning lights come on when the belt broke and the alternator stopped charging?