mkguitar has it right. On the upgrade downshift if the tranny can't seem to settle in a gear. On a downgrade, downshift so the engine provides significant braking. You don't want the brakes to overheat and fade to nothing when you need them most.
The other problem you may experience with brake heating on a downgrade is brake judder where the front end vibrates when the brakes are applied. You can still slow down but it feels like the front end is coming apart and you're losing control.