Mixtures of poly(3,4-ethylenedioxythiophene) and polystyrenesulfonate (PEDOT:PSS) have high electrical conductivity when cast from aqueous suspensions in combination with a high boiling-point cosolvent dimethyl sulfoxide (DMSO). The electronic component of the thermal conductivity of these highly conducting polymers is of interest for evaluating their potential for thermoelectric cooling and power generation. We find, using time-domain thermoreflectance measurements of thermal conductivity along multiple directions of thick (>20 μm) drop-cast PEDOT films, that the thermal conductivity can be highly anisotropic (aii ≈ 1.0 W m-1 K-1 and Aii ≈ 0.3 W m-1 K-1 for the in-plane and through-plane directions, respectively) when the electrical conductivity in the in-plane direction is large (δ ≈ 500 S cm-1). We relate the increase in thermal conductivity to the estimated electronic component of the thermal conductivity using the Wiedemann-Franz law, and find that our data are consistent with conventional Sommerfeld value of the Lorenz number. We use measurements of the elastic constants (C11 ≈ 11 GPa and C44 ≈ 17 GPa) of spin-cast PEDOT films and through-plane thermal conductivity (∧⊥ ≈ 0.3 W m-1 K-1) of drop-cast and spin-cast films to support our assumption that the phonon contribution to the thermal conductivity does not change significantly with DMSO composition.