  We study heat conduction mediated by longitudinal phonons in one dimensional
disordered harmonic chains. Using scaling properties of the phonon density of
states and localization in disordered systems, we find non-trivial scaling of
the thermal conductance with the system size. Our findings are corroborated by
extensive numerical analysis. We show that a system with strong disorder,
characterized by a `heavy-tailed' probability distribution, and with large
impedance mismatch between the bath and the system satisfies Fourier's law. We
identify a dimensionless scaling parameter, related to the temperature scale
and the localization length of the phonons, through which the thermal
conductance for different models of disorder and different temperatures follows
a universal behavior.
