  Twisted transition metal dichalcogenides (TMDs) present an intriguing
platform for exploring excitons and their transport properties. By introducing
a twist angle, a moir\'e superlattice forms, providing a spatially dependent
exciton energy landscape. Based on a microscopic many-particle theory, we
investigate in this work polaron-induced changes in exciton transport
properties in the MoSe$_2$/WSe$_2$ heterostructure. We demonstrate that polaron
formation and the associated enhancement of moir\'e excitonic mass lead to a
significant band flattening. As a result, the hopping rate and the propagation
velocity undergo noticeable temperature and twist-angle dependent changes. We
predict a reduction of the hopping strength ranging from 80% at a twist angle
of 1$^\circ$ to 30% at 3$^\circ$ at room temperature. The provided microscopic
insights into the spatio-temporal exciton dynamics in presence of a moir\'e
potential further deepens our understanding of the intriguing moir\'e exciton
physics.
