We theoretically analyze the nonlinear anomalous Nernst effect as the second-order response of temperature gradient by using the semiclassical framework of electron dynamics. We find that a nonlinear current can be generated transverse to the applied temperature gradient in time-reversal-symmetry materials with broken inversion symmetry. This effect has a quantum origin arising from the Berry curvature of states near the Fermi surface. We discuss the nonlinear Nernst effect in transition metal dichalcogenides (TMDCs) under the application of uniaxial strain. In particular, we predict that under fixed chemical potential in TMDCs, the nonlinear Nernst current exhibits a transition from T−2 temperature dependence in low temperature regime to a linear T dependence in high temperature.