  We present computational data on the thermal conductivity of nonlinear waves
in disordered chains. Disorder induces Anderson localization for linear waves
and results in a vanishing conductivity. Cubic nonlinearity restores normal
conductivity, but with a strongly temperature-dependent conductivity
$\kappa(T)$. We find indications for an asymptotic low-temperature $\kappa \sim
T^4$ and intermediate temperature $\kappa \sim T^2$ laws. These findings are in
accord with theoretical studies of wave packet spreading, where a regime of
strong chaos is found to be intermediate, followed by an asymptotic regime of
weak chaos (EPL 91 (2010) 30001).
