For the first time, the thermal conductivities of vulcanized polybutadiene and polyisoprene have been investigated according to their degree of crosslinking. The C-C and C-S-S-C crosslink bridges, which can be obtained via vulcanization processes using peroxides and sulfur, respectively, are considered. The temperature dependence of the thermal conductivity of soft rubber derived from molecular dynamics (MD) simulations is in very good agreement with the experimental results. The contributions of bonded and non-bonded interactions in the MD simulations and their influence on the thermal conductivities of polyisoprene and polybutadiene are presented. The details are discussed in this paper.