  Weyl semimetals harbor topological Fermi-arc surface states which determine
the nontrivial charge current response to external fields. We here study the
quasiparticle decay rate of Fermi arc states arising from their coupling to
acoustic phonons, as well as the phonon-limited conductivity tensor for a clean
Weyl semimetal slab. Using the phonon modes for an isotropic elastic continuum
with a deformation potential coupling to electrons, we determine the
temperature dependence of the quasiparticle decay rate, both near and far away
from the arc termination points. By solving the coupled Boltzmann equations for
the bulk and arc state distribution functions in the slab geometry, we show how
the linear response conductivity depends on key parameters such as the
temperature, the chemical potential, the geometric shape of the Fermi arcs, or
the slab width. The chiral nature of Fermi arc states causes an enhancement of
the longitudinal conductivity along the chiral direction at low temperatures,
together with a 1/T^2 scaling regime at intermediate temperatures without
counterpart for the conductivity along the perpendicular direction.
