  Dark Matter constitutes most of the matter in the presently accepted
cosmological model for our Universe. The extreme conditions of ordinary
baryonic matter, namely high density and compactness, in Neutron Stars make
these objects suitable to gravitationally accrete such a massive component
provided interaction strength between both, luminous and dark sectors, at
current experimental level of sensitivity. We consider several different DM
phenomenological models from the myriad of those presently allowed. In this
contribution we review astrophysical aspects of interest in the interplay of
ordinary matter and a fermionic light Dark Matter component. We focus in the
interior nuclear medium in the core and external layers, i.e. the crust,
discussing the impact of a novel dark sector in relevant stellar quantities for
(heat) energy transport such as thermal conductivity or emissivities.
