  The Wiedemann-Franz (WF) law links the ratio of electronic charge and heat
conductivity to fundamental constants. It has been tested in numerous solids,
but the extent of its relevance to the anomalous transverse transport, which
represents the topological nature of the wave function, remains an open
question. Here we present a study of anomalous transverse response in the
noncollinear antiferromagnet Mn$_{3}$Ge extended from room temperature down to
sub-Kelvin temperature and find that the anomalous Lorenz ratio remains close
to the Sommerfeld value up to 100 K, but not above. The finite-temperature
violation of the WF correlation is caused by a mismatch between the thermal and
electrical summations of the Berry curvature, rather than the inelastic
scattering as observed in ordinary metals. This interpretation is backed by our
theoretical calculations, which reveals a competition between the temperature
and the Berry curvature distribution. The accuracy of the experiment is
supported by the verification of the Bridgman relation between the anomalous
Ettingshausen and Nernst effects. Our results identify the anomalous Lorenz
ratio as an extremely sensitive probe of Berry spectrum near the chemical
potential.
