This paper deals with the modeling of a fully dynamic induction heating problem, considered a two-dimensional (2D) axisymmetric problem. The model is described by partial differential equations with nonlinear heat capacity, thermal and electrical conductivities. A discretization technique is applied to obtain a mathematical model in ordinary differential equation form while the nonlinearity is preserved. A model reduction technique is applied to reduce the system size. A small perturbation is given in the initial values of the original model and cumulative errors due to the perturbation and reduction calculated. The errors obtained are very small, thus illustrating the validity of the reduced model. Numerical results are presented and possible extensions are identified.