  The presence of a finite Berry curvature $\left(\Omega\left(k\right)\right)$
leads to anomalous thermal effects. In this letter, we compute the coefficients
for the anomalous Nernst effect $\left(ANE\right) $ and its spin analogue, the
spin Nernst effect $\left(SNE\right)$ in lead chalcogenide (\textit{PbX};
\textit{X} = S, Se, Te) films. The narrow gapped \textit{PbX} films with a
large spin-orbit coupling (\textit{soc}) offer a significant Rashba interaction
that gives rise to $ \Omega\left(k\right) $ and the attendant anomalous thermal
behaviour. In presence of a temperature gradient, the $ ANE $ and $ SNE $
establish a thermal and spin current and are characterized by their respective
coefficients which acquire higher values for a stronger Rashba interaction. We
further show that an extrinsic \textit{soc} generated by an in-plane electric
field offers a gate-like mechanism to control (and turn-off) the anomalous
thermal currents. Finally, we conclude by deriving the efficiency of an $ ANE
$-driven low-temperature Carnot heat engine and demonstrate that it can be
gainfully optimized in systems with a robust intrinsic \textit{soc} resulting
in low carrier effective masses.
