  The temperature ($T$) and frequency ($\omega$) dependent conductivity of
weakly disordered Luttinger liquids is calculated in a systematic way both by
perturbation theory and from a finite temperature renormalization group (RG)
treatment to leading order in the disorder strength. Whereas perturbation
theory results in $\omega/T$ scaling of the conductivity such scaling is
violated in the RG traetment. We also determine the non-linear field dependence
of the conductivity, whose power law scaling is different from that of
temperature and frequency dependence.
