  We adapt existing phonon heat transport methods to compute the phononic
thermal conductance of metallic atomic contacts during a stretching process.
Nonequilibrium molecular dynamics (NEMD) simulations are used to generate
atomic configurations and to simultaneously determine the phononic thermal
conductance. Combining the approach with established electronic structure
calculations based on a tight-binding parameterization allows us to calculate
in addition charge transport properties of each contact geometry within the
Landauer-B\"uttiker formalism. The method is computationally fast enough to
perform a statistical analysis of many stretching events, and we apply it here
to atomic junctions formed from three different metals, namely gold (Au),
platinum (Pt) and aluminum (Al). The description of both phononic and
electronic contributions to heat transport allows us to examine the validity of
the Wiedemann-Franz law at the atomic scale. We find that it is well obeyed in
the contact regime at room temperature for Au and Al as far as only electronic
contributions are concerned, but deviations of up to 10% arise for Pt. If the
total thermal conductance is studied, deviations of typically less than 10%
arise for Au and Al, which can be traced back mainly to phononic contributions
to the thermal conductance, while electronic and phononic contributions can add
up to some 20% for single-atom contacts of Pt.
