  We study black hole evaporation of near-extremal black holes in spherically
reduced models with asymptotically Minkowskian spacetime, with the effects of
the back-reaction on the geometry included semi-classically. The stress-energy
tensor is calculated for null in-falling observers. It is shown that the
evaporation proceeds smoothly and there are no instabilities of the outer or
inner apparent horizon before the endpoint of evaporation.
