  We discuss the possibility of a gravitional Nieh-Yan anomaly of the type
$\partial_\mu j^\mu_5 =\gamma T^2{\cal T}^a\wedge {\cal T}_a$ in topological
Weyl materials, where $T$ is temperature and ${\cal T}^a$ is the effective or
emergent torsion. As distinct from the non-universal parameter $\Lambda$ in the
conventional (zero temperature) Nieh-Yan anomaly -- with canonical dimensions
of momentum -- the parameter $\gamma$ is dimensionless. This suggests that the
dimensionless parameter is fundamental, being determined by the geometry,
topology and number of the number of chiral quantum fields without any explicit
non-universal UV scales. This conforms with previous results in the literature,
as well as spectral flow calculations using torsional magnetic field at finite
temperature.
