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This article discusses a recently published methodology to determine the time-harmonic (TH) effective magnetic permeability used to simulate induction heating problems comprising non-linear and hysteretic materials. The model and its implementation in a whole multiphysics numerical scheme are first shown and calibrated with temperature-dependent magnetic measurements for simulating the specific behavior of an AISI 4340 working steel piece during the induction heating process. Then, the experimental setup designed to send ${\sim }4$ kW of heating power in steel disks is explained. The setup allows the disks to reach the austenitization and Curie temperature of steel in 30 s. The temperature distributions were measured with an infrared (IR) thermal camera and compared with the simulation both in space and time during the heating. In addition to being numerically inexpensive, the computational model successfully predicts the temperature within 10% of accuracy between $200 ^{\circ} \text{C}$ and $800 ^{\circ} \text{C}$ .