Eddy current losses in conducting plates placed in a non-uniform alternating magnetic field at cryogenic temperatures have been calculated taking into account temperature dependencies of resistivity, heat capacity and heat-transfer coefficient. The calculation method is based on a coupled solution of a quasi-stationary electromagnetic problem and a nonstationary heat-conduction equation. A simplification of the task is achieved by neglecting eddy current reaction and free space charge. In this case the problem is solved in two stages: 1) the calculation of electromagnetic field; 2) the determination of a temperature distribution in the plate. As the first boundary condition for heat-conduction equation it is assumed that the heat transfer from edges of the plate equals zero. The second boundary condition is determined as a solution of the integral equation describing the law of conservation of energy relevant to the plate. The nonlinear two-dimensional heat conduction equation has been solved using partition of coordinates, implicit difference approximation and modified Thomas algorithm for obtained finite-difference equations. The numerical results remain in a good agreement with data obtained by means of an experimental model of the cryogenic device, while neglecting of thermal processes results in substantial errors amounting up to several hundreds percent.