  Path integral quantization of dilaton gravity in two dimensions is applied to
the CGHS model to the first nontrivial order in matter loops. Our approach is
background independent as geometry is integrated out exactly. The result is an
effective shift of the Killing norm: the apparent horizon becomes smaller. The
Hawking temperature which is constant to leading order receives a quantum
correction. As a consequence, the specific heat becomes positive and
proportional to the square of the black hole mass.
