  Radiating black holes pose a number of puzzles for semiclassical and quantum
gravity. These include the transplanckian problem -- the nearly infinite
energies of Hawking particles created near the horizon, and the final state of
evaporation. A definitive resolution of these questions likely requires robust
inputs from quantum gravity. We argue that one such input is a quantum bound on
curvature. We show how this leads to an upper limit on the redshift of a
Hawking emitted particle, to a maximum temperature for a black hole, and to the
prediction of a Planck scale remnant.
