  The effect of inclusion of the planar phonon anisotropy on thermo-electrical
behavior of graphene is analyzed. Charge transport is simulated by means of
Direct Simulation Monte Carlo technique coupled with numerical solution of the
phonon Boltzmann equations based on deterministic methods.
  The definition of the crystal lattice local equilibrium temperature is
investigated as well and the results furnish possible alternative approaches to
identify it starting from measurements of electric current density, with
relevant experimental advantages, which could help to overcome the present
difficulties regarding thermal investigation of graphene.
  Positive implications are expected for many applications, as the field of
electronic devices, which needs a coherent tool for simulation of charge and
hot phonon transport; the correct definition of the local equilibrium
temperature is in turn fundamental for the study, design and prototyping of
cooling mechanisms for graphene-based devices.
