  The conformal anomaly in curved spacetime generates a nontrivial anomalous
vertex, given by the three-point correlation function $TTT$ of the
energy-momentum tensor $T^{\mu\nu}$. We show that a temperature inhomogeneity
in a gas of charged massless particles generates, via the $TTT$ vertex, a
pressure anisotropy with respect to the axis of the temperature variation. This
very particular signature may provide an experimental access to the elusive
gravitational coefficient $b$ which determines the anomaly contribution of the
Weyl tensor to the trace of the energy-momentum tensor in curved spacetime. We
present an estimate of the pressure anisotropy both for fermionic
quasiparticles in the solid-state environment of Dirac semimetals as well as
for a quark-gluon plasma in relativistic heavy-ion collisions. In both cases,
the pressure anisotropy is small compared to the mean thermal pressure.
