  We examine the temperature dependence of thermal conductivity of one
dimensional nonlinear (anharmonic) lattices with and without on-site potential.
It is found from computer simulation that the heat conductivity depends on
temperature via the strength of nonlinearity. Based on this correlation, we
make a conjecture in the effective phonon theory that the mean-free-path of the
effective phonon is inversely proportional to the strength of nonlinearity. We
demonstrate analytically and numerically that the temperature behavior of the
heat conductivity $\kappa\propto1/T$ is not universal for 1D harmonic lattices
with a small nonlinear perturbation. The computer simulations of temperature
dependence of heat conductivity in general 1D nonlinear lattices are in good
agreements with our theoretic predictions. Possible experimental test is
discussed.
