Abstract <p>A constructive method of multicriteria optimization for nonlinear objects of engineering thermophysics with estimation in a uniform metric of precision for approximation to a specified thermal state in the numerical modeling of thermodiffusion fields is proposed. It is shown that the structure of sought program control does nor differ from the earlier found structure for linear models of controllable processes. Based on this ground, the technology developed in our earlier papers for solving multicriteria problems in nonlinear systems with distributed parameters is extended to the studied nonlinear objects on condition of selecting singular control values constant in time in the corresponding intervals of program control rather easily implementable in such approximation for the digital model of a controlled parameter. The capabilities of the proposed approach are illustrated with the example of independent interest on the numerical solution of the problem of optimizing the induction heating process by three basic technical and economic efficiency parameters with the specialized electrothermal model of a temperature field described by nonlinear thermal conductivity equations.</p>