  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 interior. 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 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 interior 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, with and without the presence of a magnetic field.
