The two-component Fermi gas is the simplest fermion system exhibiting superfluidity, and as such is relevant to topics ranging from superconductivity to quantum chromodynamics. Ultracold atomic gases provide an exceptionally clean realization of this system, where interatomic interactions and atom spin populations are both independently tuneable. Here we show that the finite-temperature phase diagram contains a region of phase separation between the superfluid and normal states that touches the boundary of second-order superfluid transitions at a tricritical point, reminiscent of the phase diagram of 3He–4He mixtures. A variation of interaction strength then results in a line of tricritical points that terminates at zero temperature on the molecular Bose–Einstein condensate side. On this basis, we argue that tricritical points are fundamental to understanding experiments on polarized atomic Fermi gases.