  We report on coupled heat and particle transport measurements through a
quantum point contact (QPC) connecting two reservoirs of resonantly
interacting, finite temperature Fermi gases. After heating one of them, we
observe a particle current flowing from cold to hot. We monitor the temperature
evolution of the reservoirs and find that the system evolves after an initial
response into a non-equilibrium steady state with finite temperature and
chemical potential differences across the QPC. In this state any relaxation in
the form of heat and particle currents vanishes. From our measurements we
extract the transport coefficients of the QPC and deduce a Lorenz number
violating the Wiedemann-Franz law by one order of magnitude, a characteristic
persisting even for a wide contact. In contrast, the Seebeck coefficient takes
a value close to that expected for a non-interacting Fermi gas and shows a
smooth decrease as the atom density close to the QPC is increased beyond the
superfluid transition. Our work represents a fermionic analog of the fountain
effect observed with superfluid helium and poses new challenges for microscopic
modeling of the finite temperature dynamics of the unitary Fermi gas.
