  We discuss string theory alpha' corrections to charged near-extremal black
3-branes/black holes in type IIB supergravity. We find that supersymmetric
global AdS_5 x S^5 geometry is not corrected to leading order in alpha', while
charged or non-extremal black 3-branes/black hole geometries receive alpha'
corrections. Following gauge theory-string theory correspondence the
thermodynamics of these geometries is mapped to the thermodynamics of large-n_c
N=4 supersymmetric Yang-Mills theory at finite (large) 't Hooft coupling with
the U(1)_R-charge chemical potential. We use holographic renormalization to
compute the Gibbs free energy and the ADM mass of the near-extremal solutions.
The remaining thermodynamic potentials are evaluated enforcing the first law of
thermodynamics. We present analytic expressions for the alpha' corrected
thermodynamics of black holes in AdS_5 x S^5 and the thermodynamics of charged
black 3-branes with identical chemical potentials for [U(1)_R]^3 charges and
large (compare to chemical potential) temperature. We compute alpha'
corrections to Hawking-Page phase transition. We find that for nonzero chemical
potential thermodynamics of near-extremal black 3-brane solution receives ln T
correction to leading order in alpha'.
