  We study theoretically how energy and heat are transferred between the
two-dimensional layers of bilayer carrier systems due to near-field interlayer
carrier interaction. We derive general expressions for the interlayer heat
transfer and thermal conductance. Approximation formulas and detailed
calculations for semiconductor and graphene based bilayers are presented. Our
calculations for GaAs, Si and graphene bilayers show that the interlayer heat
transfer can exceed the electron-phonon heat transfer below (system dependent)
finite crossover temperature. We show that disorder strongly enhances the
interlayer heat transport and pushes the threshold towards higher temperatures.
