The axial magnetic effect, i.e., the generation of an energy current parallel to an axial magnetic field coupling with opposite signs to left- and right-handed fermions is a non-dissipative transport phenomenon intimately related to the gravitational contribution to the axial anomaly. An axial magnetic field is naturally realized in condensed matter in the so called Weyl semi-metals. We show that the edge states of a Weyl semimetal at finite temperature possess a temperature dependent angular momentum in the direction of the vector potential intrinsic to the system. Such a condensed matter realization provides a plausible context for the experimental confirmation of the elusive gravitational anomaly.