  Hydrodynamic transport effectively describes the collective dynamics of
fluids with well-defined thermodynamic quantities. With enhanced
electron-electron interactions at elevated temperatures, the collective
behavior of electrons in graphene with minimal impurities can be depicted as a
hydrodynamic flow of charges. In this new regime, the well-known rules of Ohmic
transport based on a single electron picture no longer apply, necessitating the
consideration of collective electron dynamics. In particular, the hydrodynamic
analogues of Joule heating and thermal transport require consideration of the
viscous motion of the electron fluid, which has a direct impact on energy
dissipation and heat generation by the fluidic motion of charge. In this work,
we probe graphene hydrodynamics with thermal transport and find two distinct,
qualitative signatures: thermal conductivity suppression below the
Wiedemann-Franz value and viscous heating leading to magnetically-induced
redistribution of temperature. We find these two effects are coincident in
temperature and density, providing robust qualitative signatures of
hydrodynamics, despite arising from two distinct aspects of this new regime:
microscopic momentum conservation due to electron-electron scattering, and
geometry-dependent viscous dissipation. Our results mark the first observation
of viscous electronic heating in an electron fluid, providing insight for
thermal management in electronic hydrodynamic devices and offering a new
methodology for identifying hydrodynamic states in other systems.
