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.