  In light of the evidence that charge order coexists with d-wave
superconductivity in the underdoped cuprate superconductors, we investigate the
manner in which such charge order will influence the quasiparticle excitations
of the system and, in particular, the low-temperature transport of heat by
those quasiparticles. We consider a d-wave superconductor in which the
superconductivity coexists with charge density wave order of wave vector
(\pi/a,0). While the nodes of the quasiparticle energy spectrum survive the
onset of charge order, there exists a critical value of the charge density wave
order parameter beyond which the quasiparticle spectrum becomes fully gapped.
We perform a linear response Kubo formula calculation of thermal conductivity
in the low temperature (universal) limit. Results reveal the dependence of
thermal transport on increasing charge order up to the critical value at which
the quasiparticle spectrum becomes fully gapped and thermal conductivity
vanishes. In addition to numerical results, closed-form expressions are
obtained in the clean limit for the special case of isotropic Dirac nodes.
Signatures of the influence of charge order on low-temperature thermal
transport are identified.
