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Induction heating is a clear, cheap, and highly effective technology used for many industrial and commercial applications. Generally, a time-varying magnetic field produces the required heat in the workpiece with a specially designed coil. The efficiency of the heating process depends highly on the coil design and the geometrical arrangement. A detailed and accurate finite element analysis of the induction heating process usually needs to resolve a coupled thermoelastic–magnetic problem, whose parameters values depend on the solution of another field. The paper deals with a shrink-fitting process design problem: a gear should be assembled with an axe. The interesting part of this case study is given the prescribed low limits for critical stress, the temperature of the gear material, and the heat-treated wearing surfaces. A coupled finite-element-based model and a genetic algorithm-based parameter determination methodology were presented. A thermal imaging-based measurement validated the presented numerical model and parameter determination task. The results show that the proposed methodology can be used to calibrate and validate the numerical model and optimize an induction heating process. [ABSTRACT FROM AUTHOR]