A new robotic high-frequency local induction heat treatment system is studied. The system is designed to perform on-site local heat treatment on large steel components such as hydropower turbine runner. A flat spiral coil is moved by a robot arm over the area to treat. A fast numerical model is developed to predict the temperature distribution and system settings. Several numerical strategies are proposed to minimize the computation time. The model combines an equivalent circuit with thermal finite elements and the electromagnetic mutual impedance method. A simple approach based on the concept of complex permeability is proposed to model hysteresis losses. The computed power losses in the RLC circuit and the temperature field in flat paramagnetic and ferromagnetic workpieces are compared with experimental measurements. Results confirm the accuracy of the coupled thermo-electromagnetic model.