  Given the experimental evidence of charge order in the underdoped cuprate
superconductors, we consider the effect of coexisting charge order on
low-temperature thermal transport in a d-wave superconductor. Using a
phenomenological Hamiltonian that describes a two-dimensional system in the
presence of a Q=(\pi,0) charge density wave and d-wave superconducting order,
and including the effects of weak impurity scattering, we compute the
self-energy of the quasiparticles within the self-consistent Born
approximation, and calculate the zero-temperature thermal conductivity using
linear response formalism. We find that vertex corrections within the ladder
approximation do not significantly modify the bare-bubble result that was
previously calculated. However, self-consistent treatment of the disorder does
modify the charge-order-dependence of the thermal conductivity tensor, in that
the magnitude of charge order required for the system to become effectively
gapped is renormalized, generally to a smaller value.
