Despite demonstrated effectiveness in characterizing material properties or defect, the evaluation of material acoustic nonlinearity is highly prone to measurement contaminations introduced by various practical factors and the low robustness restricts its application. In order to obtain a precise quantification of the material acoustic nonlinearity in a robust manner, an approach based on the thermal fluctuations in nonlinear features of ultrasonic waves is developed. In this approach, the influence of temperature and defect on the interatomic distance is scrutinized analytically, and on this basis, the nonlinear features of ultrasonic waves linked with the temperature and defect is ascertained explicitly, whereby a thermal sensitivity index is proposed. With this thermal sensitivity index, the material acoustic nonlinearity can be evaluated without being affected by contaminations from practical sources, and therefore the defect which intensifies the material acoustic nonlinearity can be identified in a robust manner. Experimental validation corroborates the theoretical prediction, demonstrating that the proposed thermal sensitivity-based approach is capable of enhancing the robustness of material acoustic nonlinearity evaluation and defect characterization.