  We investigate the temperature effects in an imbalanced superfluid atomic
Fermi gas. We consider a bilayer system of two-component dipolar fermionic
atoms with one layer containing atoms of one component and the other layer the
atoms of other component with an imbalance between the populations of the two
components. This imbalance results in uniform and nonuniform superfluid phases
such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and
normal Fermi liquid phases for different system parameters. Using the
mean-field BCS theory together with the superfluid mass-density criterion we
classify different phases in thermodynamic phase diagram. Our results indicate
that for a dipolar Fermi system the Sarma phase is stable for large imbalance
at finite temperature below the critical temperature, and the FFLO phase is
stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The
phase diagram in the temperature and population imbalance plane indicate three
Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi
liquid phase while the other two correspond to the coexistance of the Sarma
phase, FFLO phase and normal Fermi phase for dipolar interactions.
