  We calculate the two-loop quantum corrections, including the back-reaction of
the Hawking radiation, to the one-loop effective metric in a unitary gauge
quantization of the CGHS model of 2d dilaton gravity. The corresponding
evaporating black hole solutions are analysed, and consistent semi-classical
geometries appear in the weak-coupling region of the spacetime when the width
of the matter pulse is larger then the short-distance cutoff. A consistent
semi-classical geometry also appears in the limit of a shock-wave matter. The
Hawking radiation flux receives non-thermal corrections such that it vanishes
for late times and the total radiated mass is finite. There are no static
remnants for matter pulses of finite width, although a BPP type static remnant
appears in the shock-wave limit. Semi-classical geometries without curvature
singularities can be obtained as well. Our results indicate that higher-order
loop corrections can remove the singularities encountered in the one-loop
solutions.
