In a nonlinear optical material, the refractive index varies with the optical intensity. In general thermal nonlinearity produces a de-focusing effect. In this paper we demonstrate that disorder changes the terms around and transform a de-focusing nonlinearity into a focusing one. When the thermal nonlinearity is activated, the two materials composing the optical fiber respond differently and the refractive index mismatch increases, enhancing the strength of the transversal Anderson localization. In a nutshell we demonstrate a nonlinearly enhanced transverse Anderson localization.