  We examine the effect of acoustic phonon scattering on the conductivity of
two-dimensional Dirac electrons. The temperature ($T$) dependence of the
conductivity ($\sigma$) is calculated using the electron Green's function with
damping by both the impurity ($\Gamma_0$) and phonon ($\Gamma_{\rm ph}$).For
zero or small doping, on which the present Rapid Communication focuses, $\sigma
(T)$ increases and becomes almost constant due to the competition between the
Dirac electrons and the phonon scattering. Such strange behavior of $\sigma
(T)$ is ascribed to an exotic mechanism of phonon scattering, whose momentum
space is strongly reduced in the presence of a Dirac cone. For large doping,
$\sigma$ decreases due to the interplay of the Fermi surface and the phonon.
The unconventional $T$ dependence of the resistivity $\rho (=1/\sigma)$ for
small doping is compared with that of the experiment of Dirac electrons in an
organic conductor.
