  Quantum virial expansion provides an ideal tool to investigate the
high-temperature properties of a strongly correlated Fermi gas. Here, we
construct the virial expansion in the presence of spin population imbalance. Up
to the third order, we calculate the high-temperature free energy of a unitary
Fermi gas as a function of spin imbalance, with infinitely large, attractive or
repulsive interactions. In the latter repulsive case, we show that there is no
itinerant ferromagnetism when quantum virial expansion is applicable. We
therefore estimate an upper bound for the ferromagnetic transition temperature
$T_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that
$(T_{c})_{uppper}<T_{F}$, where $T_{F}$ is the Fermi temperature at the center
of the trap. Our result for the high-temperature equations of state may
confront future high-precision thermodynamic measurements.
