We have developed a comprehensive 3D steady-state numerical model of high power Yb-doped fiber amplifiers which allows the investigation of thermally induced multimode behavior being the reason for the transversal mode instabilities phenomenon. Numerical simulations show that for the pump powers above 3 kW the refractive index grating inscribed as a result of thermo-optic effect supports an efficient energy transfer from the main mode to high order modes. Coupling of the initial Gaussian beam without any shift or tilt to the investigated amplifier leads to the preferential excitation and further growth of symmetrical high order modes (LP02, LP03). Anti-symmetrical modes are not growing. Increasing the pump power leads to stronger mode coupling which is related to the increase of the amplitude and frequency of the temperature oscillations and corresponding refractive index oscillations over the longitudinal axis of the fiber amplifier.