  We report a local minimum in thermal conductivity in twisted bilayer graphene
(TBG) at the angle of 1.08$^\circ$, which corresponds to the 'magic angle' in
the transition of several other reported properties. Within the supercell of a
moir\'e lattice, different stacking modes generate phonon scattering sites
which reduce the thermal conductivity of TBG. The thermal magic angle arises
from the competition between the delocalization of atomic vibrational
amplitudes and stresses on one hand, and the increased AA stacking density on
the other hand. The former effect weakens the scattering strength of a single
scatterer while the latter one increases the density of scatterers. The
combination of these two effects eventually leads to the apparition of the
highlighted irregularity in heat conduction. The manifestation of a magic
angle, disclosing new thermal mechanisms at nanoscale, further uncovers the
unique physics of two-dimensional materials.
