The paper presents the special software for transient FE analysis of coupled electromagnetic-thermal problems in a squirrel cage submerged motor working at cryogenic temperature. A time-stepping finite element method and transients analysis of an induction motor has been applied. The non-linearity of the magnetic circuit, the movement of the rotor, skewed slots, and the influence of temperature on electric and thermal properties of the materials has been taken into account. Developed on the basis of presented algorithm a computer program used to analyze the phenomenon of current displacement in the rotor bars of high-voltage cage induction motor working in cryogenic conditions. The results of the simulations are presented.