Extended-magnetohydrodynamics (MHD) transports magnetic flux and electron energy in high-energy-density experiments, but individual transport effects remain unobserved experimentally. Two factors are responsible in defining the transport: electron temperature and electron current. Each electron energy transport term has a direct analog in magnetic flux transport. To measure the thermally driven transport of magnetic flux and electron energy, a simple experimental configuration is explored computationally using a laser-heated pre-magnetized under-dense plasma. Changes to the laser heating profile precipitate clear diagnostic signatures from the Nernst, cross-gradient-Nernst, anisotropic conduction, and Righi-Leduc heat-flow. With a wide operating parameter range, this configuration can be used in both small and large scale facilities to benchmark MHD and kinetic transport in collisional/semi-collisional, local/non-local, and magnetized/unmagnetized regimes.