  It has been known for quite sometime that the Neutron Stars (NS) can play a
role of the Dark Matter (DM) detectors due to many uniques features of NS. We
apply these (previously developed) ideas to a specific form of the DM when it
is represented by a composite object, rather than by a local fundamental field
(such as WIMPs). To be more precise we consider the so-called axion quark
nuggets (AQN) dark matter model, when the ``non-baryonic" dark matter in fact
is made of quarks and gluons which are in dense quark phase (similar to the old
idea of the Witten's strangelets). We argue that the interaction of the AQNs
with NS material may lead to many profound observable effects, which
dramatically different from conventional picture when DM particles are
represented by weakly interacting WIMPs. In particular, we argue that the AQNs
may serve as the triggers for the magnetic reconnection to heat the NS surface.
This effect may strongly alleviate (or even completely remove) the observed
inconsistencies between the predicted and observed surface temperatures for
many old NS. This heating mechanism is always accompanied by the hard X ray
emission, which may serve as an indicator of the proposed mechanism.
