  We theoretically analyze the non-linear anomalous Nernst effect as the
second-order response of temperature gradient by using the semiclassical
framework of electron dynamics. We find that a non-linear 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 non-linear 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
non-linear Nernst current exhibits a transition from
$\textbf{j}^\text{dip}_\text{A}\sim T^{-2}$ temperature dependence in low
temperature regime to a linear $T$-dependence in high temperature.
