  We study two-dimensional dilaton gravity coupled to massless scalar fields
for static solutions. In addition to the well known black hole, we find another
class of solutions that may be understood as that of the black hole in
equilibrium with a radiation bath. We claim that there is a solution that is
qualitatively unchanged after including Hawking radiation and back-reaction and
is furthermore geodesically complete. We compute the thermodynamics of these
spacetimes and their mass. We end with a brief discussion of the linear
response about these solutions, its significance to stability and noise and a
speculation regarding the endpoint of Hawking evaporation in four dimensions.
(plain TeX; one figure, available upon request.)
