  We report a numerical investigation on the heat transfer through one
dimensional arrays of metallic nanoparticles closely spaced in a host material.
Our simulations show that the multipolar interactions play a crucial role in
the heat transport via collective plasmons. Calculations of the plasmonic
thermal conductance and of the thermal conductivity in ballistic and diffusive
regime, respectively have been carried out. (a) Using the Landauer-Buttiker
formalism we have found that, when the host material dielectric constant takes
positive values, the multipolar interactions drastically enhance by several
order of magnitude the ballistic thermal conductance of collective plasmons
compared with that of a classical dipolar chain. On the contrary, when the host
material dielectric constant takes negative values, we have demonstrated the
existence of non-ballistic multipolar modes which annihilate the heat transfer
through the chains. (b) Using the kinetic theory we have also examined the
thermal behavior of chains in the diffusion approximation. We have shown that
the plasmonic thermal conductivity of metallic nanoparticle chains can reach 1%
of the bulk metal thermal conductivity . This result could explain the
anomalously high thermal conductivity observed in many collo\"idal suspensions,
the so called nanofluids.
