  We consider coherent radiative thermal conductance of a multilayer photonic
crystal. The crystal consists of alternating layers of lossless dielectric
slabs and vacuum, where heat is conducted only through photons. We show that
such a structure can have thermal conductance below vacuum over the entire high
temperature range, due to the presence of partial band gap in most of the
frequency range, as well as the suppression of evanescent tunneling between
slabs at higher frequencies. The thermal conductance of this structure is
highly tunable by varying the thickness of the vacuum layers.
