  We study the heat conductance of hybrid superconducting junctions. Our
analysis involves single-channel junctions with arbitrary transmission as well
as diffusive connectors and shows the influence of the superconducting gaps and
phases of the contacts on the heat conductance. If the junction is diffusive,
these effects are completely quenched on average, however, we find that their
influence persists in weak-localization corrections and conductance
fluctuations. While these statistical properties strongly deviate from the
well-known analogues for the charge conductance, we demonstrate that the heat
conductance fluctuations maintain a close to universal behavior. We find a
generalized Wiedemann-Franz law for Josephson junctions with equal gaps and
vanishing phase difference.
