  In this talk we discuss the fate of the small Schwarzschild blackhole of
$AdS_5\times S^5$ using the AdS/CFT correspondence at finite temperature. The
third order $N = \infty$ phase transition in the gauge theory corresponds to
the blackhole-string transition. This singularity is resolved using a double
scaling limit in the transition region. The phase transition becomes a smooth
crossover where multiply wound Polyakov lines condense. In particular the
density of states is also smooth at the crossover. We discuss the implications
of our results for the singularity of the Lorenztian section of the small
Schwarzschild blackhole. (\it {Talk given at the 12th Regional conference in
Islamabad, Pakistan, based on hep-th/0605041})
