  Intrinsic anomalous Nernst effect (ANE), like its Hall counterpart, is
generated by Berry curvature of electrons in solids. Little is known about its
response to disorder. In contrast, the link between the amplitude of the
ordinary Nernst coefficient and the mean-free-path is extensively documented.
Here, by studying Co$_3$Sn$_2$S$_2$, a topological half-metallic semimetal
hosting sizable and recognizable ordinary and anomalous Nernst responses, we
demonstrate an anti-correlation between the amplitude of ANE and carrier
mobility. We argue that the observation, paradoxically, establishes the
intrinsic origin of the ANE in this system. We conclude that various intrinsic
off-diagonal coefficients are set by the way the Berry curvature is averaged on
a grid involving the mean-free-path, the Fermi wavelength and the de Broglie
thermal length.
