  Solutions of type IIB supergravity which preserve half of the supersymmetries
have a dual description in terms of free fermions, as elucidated by the
"bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study
the half-BPS geometry associated with a gas of free fermions in thermodynamic
equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of
low and high temperature. In the former case, we present a detailed computation
of the ADM mass of the supergravity solution and find agreement with the
thermal energy of the fermions. The solution has a naked null singularity and,
by general arguments, is expected to develop a finite area horizon once stringy
corrections are included. By introducing a stretched horizon, we propose a way
to match the entropy of the fermions with the entropy of the geometry in the
low temperature regime. In the opposite limit of high temperature, the solution
resembles a dilute gas of D3 branes. Also in this case the ADM mass of the
geometry agrees with the thermal energy of the fermions.
