  Recent advances in rapidly quenched ultracold atomic Fermi gases near a
Feshbach resonance have brought about a number of interesting problems, in the
context of observing the long-sought Stoner ferromagnetic phase transition. The
possibility of experimentally obtaining a "quasirepulsive" regime in the upper
branch of the energy spectrum due to the rapid quench is currently being
debated, and the Stoner transition has mainly been investigated theoretically
by using perturbation theory or at high polarization, due to the limited
theoretical approaches in the strongly repulsive regime. In this work, we
present a nonperturbative theoretical approach to the quasirepulsive upper
branch of a Fermi gas near a broad Feshbach resonance, and we determine the
finite-temperature phase diagram for the Stoner instability. Our results agree
well with the known quantum Monte-Carlo simulations at zero temperature, and we
recover the known virial expansion prediction at high temperature for arbitrary
interaction strengths. At resonance, we find that the Stoner transition
temperature becomes of the order of the Fermi temperature, around which the
molecule formation rate becomes vanishingly small. This suggests a feasible way
to observe Stoner ferromagnetism in the nondegenerate temperature regime.
