Analysis of heat transfer in the floating zone (FZ) crystal growth system with a radio-frequency (RF) induction heating is carried out, using the hybrid finite element and boundary element method for calculation of the electromagnetic and temperature fields, and applying the coordinate transformation method to represent exactly the unknown shapes of phase boundaries in the system. The effects of processing parameters, such as the RF current frequency, on FZ growth is investigated numerically, and a diagram for the upper and lower limits of the current density in the RF coil between which the molten zone can be stable is proposed.