  We construct the black hole geometry dual to the deconfined phase of the BMN
matrix model at strong 't Hooft coupling. We approach this solution from the
limit of large temperature where it is approximately that of the non-extremal
D0-brane geometry with a spherical $S^8$ horizon. This geometry preserves the
$SO(9)$ symmetry of the matrix model trivial vacuum. As the temperature
decreases the horizon becomes deformed and breaks the $SO(9)$ to the
$SO(6)\times SO(3)$ symmetry of the matrix model. When the black hole free
energy crosses zero the system undergoes a phase transition to the confined
phase described by a Lin-Maldacena geometry. We determine this critical
temperature, whose computation is also within reach of Monte Carlo simulations
of the matrix model.
