  We study through holography the compact Randall-Sundrum (RS) model at finite
temperature. In the presence of radius stabilization, the system is described
at low enough temperature by the RS solution. At high temperature it is
described by the AdS-Schwarzschild solution with an event horizon replacing the
TeV brane. We calculate the transition temperature T_c between the two phases
and we find it to be somewhat smaller than the TeV scale. Assuming that the
Universe starts out at T >> T_c and cools down by expansion, we study the rate
of the transition to the RS phase. We find that the transition is very slow so
that an inflationary phase at the weak scale begins. The subsequent evolution
depends on the stabilization mechanism: in the simplest Goldberger-Wise case
inflation goes on forever unless tight bounds are satisfied by the model
parameters; in slightly less-minimal cases these bounds may be relaxed.
