  Heating and heat conduction in molecular junctions are considered within a
general NEGF formalism. We obtain a unified description of heating in current
carrying molecular junctions as well as the electron and phonon contributions
to the thermal flux, including their mutual influence. Ways to calculate these
contributions, their relative importance and ambiguities in their definitions
are discussed. A general expression for the phonon thermal flux is derived and
used in a new "measuring technique", to define and quantify 'local temperature'
in nonequilibrium systems. Superiority of this measuring technique over the
usual approach that defines effective temperature using the equilibrium phonon
distribution is demonstrated. Simple bridge models are used to illustrate the
general approach, with numerical examples.
