  We study the supergravity dual to the confinement/deconfinement phase
transition for the N=4 SU(N) SYM on R x S^3 with a chemical potential conjugate
to a U(1)\subset SO(6)_R charge. The appropriate supergravity system is a
single charge black hole in D=5 N=8 gauged supergravity. Application of the
gauge/string theory holographic renormalization approach leads to new
expressions for the black hole ADM mass and its generalized free energy. We
comment on the relation of this phase transition to the Hagedorn transition for
strings in the maximally supersymmetric plane wave background with null RR five
form field strength.
