  Cross-plane electrical and thermal transport in thin films of a conducting
polymer (poly(3,4-ethylenedioxythiophene), PEDOT) stabilized with
trifluoromethanesulfonate (OTf) is investigated in this study. We explore their
electrical properties by conductive atomic force microscopy (C-AFM), which
reveals the presence of highly conductive nano-domains. Thermal conductivity in
cross-plane direction is measured with Null-Point scanning thermal microscopy
(NP-SThM): PEDOT:OTf indeed demonstrates non-negligible electronic contribution
to the thermal transport. We further investigate the correlation between
electrical and thermal conductivity by applying posttreatment: chemical
reduction (de-doping) for the purpose of lowering charge carrier concentration
and hence, electrical conductivity and acid treatment (over-doping) to increase
the latter. From our measurements, we find a vibrational thermal conductivity
of 0.34 (+/- 0.04) Wm-1 K-1. From the linear dependence or the electronic
contribution of thermal conductivity vs. the electronic conductivity
(Widemann-Franz law), we infer a Lorenz number 6 times larger than the
classical Sommerfeld value as also observed in many organic materials for
in-plane thermal transport. Applying the recently proposed molecular
Widemann-Franz law, we deduced a reorganization energy of 0.53 (+/- 0.06) eV.
