  In this paper, we find the heat capacity of the magnetic dual chiral density
wave (MDCDW) phase of dense quark matter and use it to explore the feasibility
of this phase for a neutron star core. MDCDW is a spatially inhomogeneous phase
of quark matter known to be favored at intermediate densities over the chirally
symmetric phase and the color-flavor-locked superconducting phase. By comparing
our result to the lower limit of the core heat capacity established from
observations of transiently-accreting neutron stars, we show that the heat
capacity of a core made of MDCDW quark matter is well above that lower limit
and hence cannot be ruled out. This result adds to a wealth of complementary
investigations, all of which has served to strengthen the viability of a
neutron star core made of MDCDW quark matter. For completeness, we review the
contributions to the heat capacity of the main neutron-star ingredients at low,
high and intermediate densities.
