  We study the finite temperature $T$ behavior of trapped Fermi gases as they
undergo BCS-Bose Einstein condensation (BEC) crossover, in the presence of a
population imbalance. Our results, in qualitative agreement with recent
experiments, show how the superfluid phase transition is directly reflected in
the particle density profiles. We demonstrate that at $ T \neq 0$ and in the
near-BEC and unitary regimes, the polarization is excluded from the superfluid
core. Nevertheless a substantial polarization fraction is carried by a normal
region of the trap having strong pair correlations, which we associate with
noncondensed pairs or the ``pseudogap phase''.
