  We study thermal effects on equations of state (EOS) in isospin QCD,
utilizing a quark-meson model coupled to a Polyakov loop. The quark-meson model
is analyzed at one-loop that is the minimal order to include quark substructure
constraints on pions which condense at finite isospin density. In the previous
study we showed that the quark-meson model at zero temperature produces the
sound velocity peak and the negative trace anomaly in the domain between the
chiral effective theory regime at low density and the perturbative QCD regime
at high density, in reasonable agreement with lattice simulations. We now
include thermal effects from quarks in the Polyakov loop background and examine
EOS, especially the sound velocity and trace anomaly along isentropic
trajectories. At large isospin density, there are three temperature windows;
(i) the pion condensed region with almost vanishing Polyakov loops, (ii) the
pion condensed region with finite Polyakov loops, and (iii) the quark gas
without pion condensates. In the domain (i), the gap associated with the pion
condensate strongly quenches thermal excitations. As the system approaches the
domain (ii), thermal quarks, which behave as non-relativistic particles, add
energy density but little pressure, substantially reducing the sound velocity
to the value less than the conformal value while increasing the trace anomaly
toward the positive value. Approaching the domain (iii), thermal quarks become
more relativistic as pion condensates melt, increasing sound velocity toward
the conformal limit. Corrections from thermal pions are also briefly discussed.
