  In metallic ferromagnets, the Berry curvature of underlying quasiparticles
can cause an electric voltage perpendicular to both magnetization and an
applied temperature gradient, a phenomenon called the anomalous Nernst effect
(ANE). Here, we report the observation of a giant ANE in the full-Heusler
ferromagnet Co$_2$MnGa, reaching $S_{yx}\sim -6$ $\mu$V/K at room $T$, one
order of magnitude larger than the maximum value reported for a magnetic
conductor. With increasing temperature, the transverse thermoelectric
conductivity or Peltier coefficient $\alpha_{yx}$ shows a crossover between
$T$-linear and $-T \log(T)$ behaviors, indicating the violation of Mott formula
at high temperatures. Our numerical and analytical calculations indicate that
the proximity to a quantum Lifshitz transition between type-I and type-II
magnetic Weyl fermions is responsible for the observed crossover properties and
an enhanced $\alpha_{yx}$. The $T$ dependence of $\alpha_{yx}$ in experiments
and numerical calculations can be understood in terms of a quantum critical
scaling function predicted by the low energy effective theory over more than a
decade of temperatures. Moreover, the observation of chiral anomaly or an
unsaturated positive longitudinal magnetoconductance also provide evidence for
the existence of Weyl fermions in Co$_2$MnGa.
