  Two conducting quantum systems coupled only via interactions can exhibit the
phenomenon of Coulomb drag, in which a current passed through one layer can
pull a current along in the other. However, in systems with particle-hole
symmetry -- for instance, the half-filled Hubbard model or graphene near the
Dirac point -- the Coulomb drag effect vanishes to leading order in the
interaction. Its thermal analogue, whereby a thermal current in one layer pulls
a thermal current in the other, does not vanish and is indeed the dominant form
of drag in particle-hole symmetric systems. By studying a quantum quench, we
show that thermal drag, unlike charge drag, displays a non-Fermi's Golden Rule
growth at short times due to a logarithmic scattering singularity generic to
one dimension. Exploiting the integrability of the Hubbard model, we obtain the
long-time limit of the quench for weak interactions. Finally, we comment on
thermal drag effects in higher dimensional systems.
