Beyond Stefan-Boltzmann Law: Thermal Hyper-Conductivity
  We demonstrate that the broadband divergence of the photonic density of states in hyperbolic metamaterials leads to giant increase in radiative heat transfer, beyond the limit set by the Stefan-Boltzmann law. The resulting radiative thermal "hyper-conductivity" may approach or even exceed heat conductivity via electrons and phonons in regular solids. 
Evgenii E. Narimanov and Igor I. Smolyaninov
physics.optics cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.other