  We discuss some aspects of the behaviour of a string gas at the Hagedorn
temperature from a Euclidean point of view. Using AdS space as an infrared
regulator, the Hagedorn tachyon can be effectively quasi-localized and its
dynamics controled by a finite energetic balance. We propose that the off-shell
RG flow matches to an Euclidean AdS black hole geometry in a generalization of
the string/black-hole correspondence principle. The final stage of the RG flow
can be interpreted semiclassically as the growth of a cool black hole in a
hotter radiation bath. The end-point of the condensation is the large Euclidean
AdS black hole, and the part of spacetime behind the horizon has been removed.
In the flat-space limit, holography is manifest by the system creating its own
transverse screen at infinity. This leads to an argument, based on the
energetics of the system, explaining why the non-supersymmetric type 0A string
theory decays into the supersymmetric type IIB vacuum. We also suggest a notion
of `boundary entropy', the value of which decreases along the line of flow.
