  This is the second part of a project on the foundations of first-principle
calculations of the electron transport in crystals at finite temperatures,
aiming at a predictive first-principles platform that combines ab-initio
molecular dynamics (AIMD) and a finite-temperature Kubo-formula with
dissipation for thermally disordered crystalline phases. The latter are encoded
in an ergodic dynamical system $(\Omega,\mathbb G,{\rm d}\mathbb P)$, where
$\Omega$ is the configuration space of the atomic degrees of freedom, $\mathbb
G$ is the space group acting on $\Omega$ and ${\rm d}\mathbb P$ is the ergodic
Gibbs measure relative to the $\mathbb G$-action. We first demonstrate how to
pass from the continuum Kohn-Sham theory to a discrete atomic-orbitals based
formalism without breaking the covariance of the physical observables w.r.t.
$(\Omega,\mathbb G,{\rm d}\mathbb P)$. Then we show how to implement the
Kubo-formula, investigate its self-averaging property and derive an optimal
finite-volume approximation for it. We also describe a numerical innovation
that made possible AIMD simulations with longer orbits and elaborate on the
details of our simulations. Lastly, we present numerical results on the
transport coefficients of crystal silicon at different temperatures.
