  We study the electrical conductivity of hot Abelian plasma containing scalar
charge carriers in the leading logarithmic order in coupling constant $\alpha$
using the Boltzmann kinetic equation. The leading contribution to the collision
integral is due to the M{\o}ller and Bhabha scattering of scalar particles with
a singular cross section in the region of small momentum transfer. Regularizing
this singularity by taking into account the hard thermal loop corrections to
the propagators of intermediate particles, we derive the second order
differential equation which determines the kinetic function. We solve this
equation numerically and also use a variational approach in order to find a
simple analytical formula for the conductivity. It has the standard parametric
dependence on the coupling constant $\sigma\approx 2.38\, T/(\alpha
\log\alpha^{-1})$ with the prefactor taking a somewhat lower value compared to
the fermionic case. Finally, we consider the general case of hot Abelian plasma
with an arbitrary number of scalar and fermionic particle species and derive
the simple analytical formula for its conductivity.
