So in essence you are describing the effect of hot electrons, which usually is very small. In the tutorial I referred to, the main effect is observed when the electrodes is at different temperatures, but also the thermionic effect is larger for larger tunnel distances.
ATK 13.8 can compute phonon frequencies and phonon transport, but electron-phonon interaction is not yet included.
In theory you can do DFT-MD but it's extremely time-consuming, so the sensible choice for mechnical properties is surely classical MD. ATK 13.8 introduces many new functionalities in this area, such as the Tersoff potential, NPT, and a few other things.