The nature of turbulent transport in tokamak plasmas results in temperature profiles that are called resilient or stiff, and the stabilization of magnetic islands by a localized heat source is expected to be extremely sensitive to the stiffness strength. Theoretical expectations are verified with nonlinear simulations, showing a good agreement and confirming the enhanced stabilization efficiency due to large profile stiffness, when the power used for the control is small compared with the heating power producing the equilibrium profiles. Heat sources, which are present in the island region before RF heating is applied, contribute to reducing the island size, but at the same time, severely dampen the control capability.