  We introduce a variant of the Banded Random Matrix ensemble and show, using
detailed numerical analysis and theoretical arguments, that the phonon heat
current in disordered quasi-one-dimensional lattices obeys a one-parameter
scaling law. The resulting beta-function indicates that an anomalous Fourier
law is applicable in the diffusive regime, while in the localization regime the
heat current decays exponentially with the sample size. Our approach opens a
new way to investigate the effects of Anderson localization in heat conduction,
based on the powerful ideas of scaling theory.
