The austenite Fe-Cr steels used as the critical in-pile components because of its good high temperature resistance, corrosion resistance and excellent mechanical properties and thermal strength, bear long-period high temperatures and irradiation; the irradiated vacancies aggregate into voids leading to irradiation swelling and hardening, which seriously affects the service safety of the reactor. The phase field method coupling temperature field is employed by solving the phase field equations based the Fourier spectrum method to investigate the voids behavior of austenite Fe-Cr steels upon a central and a one-dimensional temperature field. As the temperature goes down from the center radically in a central temperature field, the vacancies diffuse toward the high-temperature center region driven by the temperature gradient, resulting in the instability of the double voids model, and gradually dissolves to form a new void in the high temperature center region. In the central temperature field, the voids nucleate earlier and grow faster with a sizeable scale in the high temperature than that in the lower temperature region due to the higher vacancy concentration in the central high temperature region. Based on the force-flow relation in the principle of irreversible thermodynamics, the migration behavior of voids upon a one-dimensional temperature gradient is studied by adding advection term to the phase field evolution equation Cahn-Hilliard equation. It has been observed in the experiments that the size of voids in irradiated austenite Fe-Cr steel is nanoscale, and it is generally believed that the nanoscale voids migration is controlled by the bulk diffusion mechanism and surface diffusion mechanism. Therefore, the effects of temperature gradient and initial size of voids on the voids migration upon a one-dimensional temperature gradient in austenite Fe-Cr steel are studied considering both the bulk diffusion mechanism and surface diffusion mechanism respectively. The migration rate governed by the bulk diffusion mechanism positively depends on the temperature gradients but not the initial void"s size. The migration rate governed by the surface diffusion mechanism positively depends on the temperature gradients but is negatively related to the initial void"s size. At the same time, in the process of migration, the shape of the void will also change, and the void will be elongated along the direction of temperature gradient, and the front end is sharper along the direction of temperature gradient, and the back end is wider. The studies inspire the microstructure aging and properties prediction caused by inhomogeneous heat conduct or macroscopic uneven temperature distribution.