  We describe how the reduced phase space quantization of the CGHS model of 2d
black hole formation allows one to calculate the backreaction up to any finite
order in matter loops. We then analyze the backreaction in the Hawking
radiation up to two loops. At one-loop order the Hawking temperature does not
change, while at two-loop order the temperature increases three times with
respect to the classical value. We argue that such a behavior is consistent
with the behaviour of the operator quantization Hawking flux for times which
are not too late. For very late times the two-loop flux goes to zero which
indicates that the backreaction can stop the black hole evaporation.
