  This investigation explores the phononic thermal conductivity of nuclear star
matter as it undergoes the "topological" transition to the "pasta" regime, and
further down to the solid-liquid phase transition. The study was carried out
using molecular dynamics simulations with nuclear potentials embedded in an
effective (i.e. Thomas-Fermi) Coulomb potential. The thermal conductivity
experiences a dramatic change within a narrow temperature interval around T=1
MeV. This change accomplishes the "pasta" breakdown during a heating process.
The thermal conductivity by flipping protons' or neutrons' velocity further
shows a decoupling for asymmetric nuclear star matter.
