Early time kinetics of a system with conserved order parameter quenched int
o an unstable two-phase region of the phase diagram is considered. We study
the process of phase separation under the influence of random "frozen-in"
inhomogeneities of mobility. The combined effect of this "frozen-in" random
ness and persistent thermal fluctuations on the structure factor is discuss
ed. The maximum instability of the Cahn-Hilliard type shifts to larger wave
lengths, which may be interpreted as "coarsening" even for small times.