  We show that AdS black holes dual to field theories on flat spacetime, as
used in applications of the AdS/CFT correspondence to strong interaction and
condensed matter physics, have temperatures with positive lower bounds. There
are two distinct effects involved. For low chemical potentials in the dual
field theory, the cooling black hole makes a transition to a state
corresponding to confinement in the field theory. For high chemical potentials,
it becomes unstable to a non-perturbative string effect. This allows a
holographic sketch of the field theory phase diagram, one which is in
qualitative agreement with the phenomenological understanding of the theory at
[relatively] low temperatures. It also puts an interesting upper bound on the
temperature-normalized chemical potential $\bar{\mu}$ of the field theory, if
it describes a plasma: in the normalization of Myers et al., $\bar{\mu}$ must
be less than approximately 0.49. Thus, the extent to which a chemical potential
can worsen violations of the KSS bound is severely restricted.
