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We investigate the finite temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a non-polarized Bardeen-Cooper-Schriffer superfluid (PP_c), depending on the smallness of the spin polarization P,doi:10.1103/physreva.78.023601 fatcat:d6mg4sr56bfkxai7zcgv7ow4aq