[Deweybill]

The rear brakes heat up while going UP a steep winding grade at slow speed on my 2006 Prius. Any ideas what could cause this?

 

[Tideland Prius]

The parking brake was left engaged?

 

[David Beale]

If the road was wet it could be the vehicle stability system. It applies individual brakes to keep the vehicle from sliding.

 

[DanMan32]

If that were the case though, you'd see a blinking yellow picture of a car with sqiggly lines under it on your dash. It comes on with ABS or TC, and will be on accompanied by beeps with VSC.

You may need the brakes readjusted, they may have been set or became too tight.