  Time-dependent specific heat experiments on the molecular nanomagnet Fe8 and
the isotopic enriched analogue 57Fe8 are presented. The inclusion of the 57Fe
nuclear spins leads to a huge enhancement of the specific heat below 1 K,
ascribed to a strong increase in the spin-lattice relaxation rate Gamma arising
from incoherent, nuclear-spin-mediated magnetic quantum tunneling in the
ground-doublet. Since Gamma is found comparable to the expected tunneling rate,
the latter process has to be inelastic. A model for the coupling of the
tunneling levels to the lattice is presented. Under transverse field, a
crossover from nuclear-spin-mediated to phonon-induced tunneling is observed.
