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The area of coupled problems has been receiving substantial amount of attention over the last decade. An important class of coupled field problems involves electromagnetic-thermal coupling. Induction heating systems, where this coupling can be found, is preferred in modern industry for its efficiency, precise control, rapid control and low pollution. Optimization and control of such systems has received much attention lately. The underlying electromagnetic and thermal processes are usually modeled by finite element modeling (FEM) technique, particularly when the geometries of the work pieces involved are complicated. Simulation of such models involves heavy time stepping computations often involving several thousand time-varying variables. However the actual dynamics of interest are between only a few of the variables for which model reduction strategy based on Krylov-subspace projection provides a promising alternative. Based on this, a modeling and simulation strategy is presented for induction heating systems, involving a two-stage model reduction process. It significantly extends an earlier reported approach. Numerical results are presented for a generic induction heating system with promising results, illustrating the performance of the strategy compared to conventional FE time-step computations.