  We calculate the thermal conductivity of electrons and muons kappa_{e-mu}
produced owing to electromagnetic interactions of charged particles in neutron
star cores and show that these interactions are dominated by the exchange of
transverse plasmons (via the Landau damping of these plasmons in
nonsuperconducting matter and via a specific plasma screening in the presence
of proton superconductivity). For normal protons, the Landau damping strongly
reduces kappa_{e-mu} and makes it temperature independent. Proton
superconductivity suppresses the reduction and restores the Fermi-liquid
behavior kappa_{e-mu} ~ 1/T. Comparing with the thermal conductivity of
neutrons kappa_n, we obtain kappa_{e-mu}> kappa_n for T>2 GK in normal matter
and for any T in superconducting matter with proton critical temperatures
T_c>3e9 K. The results are described by simple analytic formulae.
