  We study the heat conductivity in Anderson insulators in the presence of
power-law interaction. Particle-hole excitations built on localized electron
states are viewed as two-level systems randomly distributed in space and energy
and coupled due to electron-electron interaction. A small fraction of these
states form resonant pairs that in turn build a complex network allowing for
energy propagation. We identify the character of energy transport through this
network and evaluate the thermal conductivity. For physically relevant cases of
2D and 3D spin systems with $1/r^3$ dipole-dipole interaction (originating from
the conventional $1/r$ Coulomb interaction between electrons), the found
thermal conductivity $\kappa$ scales with temperature as $\kappa\propto T^3 $
and $\kappa\propto T^{4/3}$, respectively. Our results may be of relevance also
to other realizations of random spin Hamiltonians with long-range interactions.
