  In contrary to other 1D momentum-conserving lattices such as the
Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice, the 1D coupled rotator lattice
is a notable exception which conserves total momentum while exhibits normal
heat conduction behavior. The temperature behavior of the thermal
conductivities of 1D coupled rotator lattice had been studied in previous works
trying to reveal the underlying physical mechanism for normal heat conduction.
However, two different temperature behaviors of thermal conductivities have
been claimed for the same coupled rotator lattice. These different temperature
behaviors also intrigue the debate whether there is a phase transition of
thermal conductivities as the function of temperature. In this work, we will
revisit the temperature dependent thermal conductivities for the 1D coupled
rotator lattice. We find that the temperature dependence follows a power law
behavior which is different with the previously found temperature behaviors.
Our results also support the claim that there is no phase transition for 1D
coupled rotator lattice. We also give some discussion about the similarity of
diffusion behaviors between the 1D coupled rotator lattice and the single
kicked rotator also called the Chirikov standard map.
