  It is well known that one-loop free energy of closed strings diverges above
the Hagedorn temperature. One explanation for this divergence is that a
`winding mode' in the Euclidean time direction becomes tachyonic above the
Hagedorn temperature. The Hagedorn transition of closed strings has been
proposed as a phase transition via condensation of this winding tachyon.
However, we have not known the stable minimum of the potential of this winding
tachyon so far. On the other hand, we have previously calculated the finite
temperature effective potential of open strings on D-brane--anti-D-brane pairs,
and shown that a phase transition occurs near the Hagedorn temperature and
D9-brane--anti-D9-brane pairs become stable. In this paper, we present a
conjecture that {\it D9-brane--anti-D9-brane pairs are created by the Hagedorn
transition of closed strings}, and describe some circumstantial evidences. We
compute two types of the cylinder amplitudes of open strings and show that
these amplitudes approach to the sphere amplitude of closed strings with two
winding tachyon insertion in the closed string vacuum limit together with the
Hagedorn temperature limit. We also show that the potential energy at the open
string vacuum decreases limitlessly as the temperature approaches to the
Hagedorn temperature. It is natural to think that the open string vacuum
becomes the global minimum near the Hagedorn temperature.
