  We calculate the thermal conductivity of various moir\'e bilayer systems
using a continuum approach and the semiclassical transport theory. When the
twist angle is close to 0, we observe a significant reduction of thermal
conductivity in a particular low-temperature regime. This reduction is
attributed to a moir\'e-induced reconstruction of acoustic phonon bands and
associated decrease of the group velocity. Conversely, in the zero temperature
limit, the thermal conductivity is enhanced by moir\'e effect, surpassing the
original values in non-moir\'e counterparts. These changes result in a
characteristic temperature dependence which deviates from the quadratic
behavior in intrinsic two-dimensional systems.
