  We compute the low-temperature behavior of the specific heat of normal
(non-color-superconducting) degenerate quark matter as well as that of an
ultradegenerate electron gas. Long-range magnetic interactions lead to
non-Fermi-liquid behavior with an anomalous leading $T\ln T^{-1}$ term.
Depending on the thermodynamic potential used as starting point, this effect
appears as a consequence of the logarithmic singularity in the fermion
self-energy at the Fermi surface or directly as a contribution from the only
weakly screened quasistatic magnetic gauge bosons. We show that a calculation
of Boyanovsky and de Vega claiming the absence of a leading $T\ln T^{-1}$ term
missed it by omitting vector boson contributions to the internal energy. Using
a formulation which collects all nonanalytic contributions in bosonic ring
diagrams, we systematically calculate corrections beyond the well-known
leading-log approximation. The higher-order terms of the low-temperature
expansion turn out to also involve fractional powers $T^{(3+2n)/3}$ and we
explicitly determine their coefficients up to and including order $T^{7/3}$ as
well as the subsequent logarithmically enhanced term $T^3 \ln (c/T)$. We derive
also a hard-dense-loop resummed expression which contains the infinite series
of anomalous terms to leading order in the coupling and which we evaluate
numerically. At low temperatures, the resulting deviation of the specific heat
from its value in naive perturbation theory is significant in the case of
strongly coupled normal quark matter and thus of potential relevance for the
cooling rates of (proto-)neutron stars with a quark matter component.
