Electron and muon thermal conductivity of dense matter (rho greater than or similar to 10(14) g.cm(-3)) in neutron star cores with various nuclear compositions (n, p, e, mu and possibly hyperons) is calculated. The effects of nucleon (and/or hyperon) superfluidity are taken into account. In non-superfluid matter, the main scattering mechanism of electrons and muons is the Coulomb scattering on charged baryons. If the baryon component of matter is highly superfluid, ee, e mu and mu mu collisions dominate. The results are described by simple analytic expressions valid for a wide class of models of dense matter.