  The world volume theory on $N$ regular and $M$ fractional D3-branes at the
conifold singularity is a non-conformal ${\cal N}=1$ supersymmetric
$SU(N+M)\times SU(N)$ gauge theory. In previous work the extremal Type IIB
supergravity dual of this theory at zero temperature was constructed.
Regularity of the solution requires a deformation of the conifold: this is a
reflection of the chiral symmetry breaking. To study the non-zero temperature
generalizations non-extremal solutions have to be considered, and in the high
temperature phase the chiral symmetry is expected to be restored. Such a
solution is expected to have a regular Schwarzschild horizon. We construct an
ansatz necessary to study such non-extremal solutions and show that the
simplest possible solution has a singular horizon. We derive the system of
second order equations in the radial variable whose solutions may have regular
horizons.
