We study the evaporation process of 2D black holes in thermal equilibr
ium when the incoming radiation is turned off. Our analysis is based o
n two different classes of 2D dilaton gravity models which are exactly
solvable in the semiclassical approximation including back-reaction.
We consider a one parameter family of models interpolating between the
Russo-Susskind-Thorlacius and Bose-Parker-Peleg models. We find that
the end-state geometry is the same as the one coming from an evaporati
ng black hole formed by gravitational collapse. We also study the quan
tum evolution of black holes arising in a model with classical action
S = 1/2 pi integral d(2)x root-g (R phi + 4 lambda 2e(beta phi)). The
black hole temperature is proportional to the mass and the exact semic
lassical solution indicates that these black holes never disappear com
pletely.