  The optical and Boltzmann conductivities have been calculated for doped
buckled honeycomb lattice structures such as silicene and germanene, as
functions of temperature. By making use of previous results for the
temperature-dependent chemical potential for gapped Dirac systems, we have
calculated the dynamical polarization function and investigated the way in
which initial doping affects its behavior at arbitrary temperature, frequency
and wave number. We have calculated the optical and Boltzmann conductivities in
the relaxation time approximation. Both these quantities are directly related
to the polarizability, with the former being proportional to its
long-wavelength limit, whereas the latter depends on static screening and the
corresponding dielectric function. We demonstrated that initial doping
substantially increases each type of conductivity at intermediate temperatures
and we have introduced a formalism for calculating the inverse relaxation time
and transition rates for the two inequivalent subbands in silicene.
