The thermal conductivity of amorphous atactic polystyrene (PS) swollen in supercritical carbon dioxide (sc CO2) has been investigated over wide temperature, pressure, and concentration ranges. Nonequilibrium molecular dynamics simulations with a full atomistic force field have been used to calculate the thermal conductivity of neat PS and sc CO2 as well as of the binary system at different compositions. An analytical interpolation formula for the thermal conductivity of the binary mixture on the basis of PS and CO2 data has been obtained. Particular attention has been paid to the implications of the quasi-degeneracy and finite-size effects in the simulated polymer system. It has been found that, in addition to the degrees of freedom per volume, the orientation of the carbon-carbon bonds in the backbone relative to the direction of the temperature gradient is important for the heat transport in PS.