The impurity relaxation via spin diffusion is effective when the local inverse spin temperature near defects, *loc, is closer to the equilibrium value equal to the inverse lattice temperature, *l, than the average value over the sample, <*>. If the spin-lattice relaxation time is measured using the conventional saturation recovery procedure, the impurity relaxation proceeds under the condition *loc > <*>. A rather strong additional magnetic (as well as acoustic or electric) steady saturation produces local heating of the nuclear spin-system, corresponding to *loc = 0 while <*> is equal to a steady-state value <*>st > 0. This means that the regions near impurities become warmer than the spin-system in the main crystal volume. In this case, the impurity relaxation should be turned off and the restoration of the magnetization in the sample should be caused by the lattice mechanism only.