The clamping technology based on high-speed induction heating of the fixing part of the system is proposed and analyzed. The continuous mathematical model of the clamping process is given by three partial differential equations (PDEs) describing the distributions of electromagnetic field, temperature field and field of thermoelastic displacements. Their coefficients containing the physical parameters of the materials are nonlinear temperature-dependent functions. The system is solved numerically in the hard-coupled formulation using a fully adaptive higher-order finite element method developed by the hp-FEM group and implemented in the application Agros2D. The methodology is illustrated with a practical example of fixing the shank of a high-revolution drilling tool in the clamping head. The results are verified by experiments.