Liquid crystals are of great interest in the field of nonlinear optics due to their efficient response to low intensity light fields. Here we present a new, to the best of our knowledge, mechanism of a nonlinear optical response which is observed for a dye-doped dual-frequency nematic liquid crystal. The local increase in temperature caused by the absorption of light beam in the liquid crystal medium leads to spatial variation and inversion of the sign of the dielectric anisotropy. When an alternating current electric field with a frequency close to the cross-over frequency is applied to the liquid crystal cell, the planar orientation sustains at the beam periphery, but elastic deformation occurs in the irradiation region. In the case of a dye dopant with negative absorption dichroism, a first-order orientational transition with large bistability region is obtained.