  We study the thermal transport properties of twisted-layer graphite
nanofibers. We show that in the presence of a twisted layer, the phonon thermal
conductance of a graphite nanofiber varies remarkably with the twisted angle
and can reach minimum values either at two critical angles $\theta_1$ and
$\theta_2$ that conform to the rule $\theta_1$ + $\theta_1$ = $180^0$ or
exactly at the angle $\theta$ = $90^0$. A reduction of roughly 50% of the
phonon thermal conductance can be achieved in some structures. We unveil that
the twisting effect mainly influences the optical modes, leaving almost
unaltered the acoustic ones. The effect is also visible in the higher and more
numerous van Hove singularities of the phonon density of states. We also point
out that the behavior of the thermal conductance with the twisted angle is
associated with and dominated by the alteration in the overlap area between the
twisted and non-twisted layers. The finite-size effect is demonstrated to play
an essential role in defining the critical angles at the local minimums, where
these angles are dependent on the size of the investigated nanofibers, in
particular on the proportion between the widths of zigzag and armchair edges.
