  We study the thermal Casimir effect between two thick slabs composed of
plane-parallel layers of random dielectric materials interacting across an
intervening homogeneous dielectric. It is found that the effective interaction
at long distances is self averaging and is given by a description in terms of
effective dielectric functions. The behavior at short distances becomes random
(sample dependent) and is dominated by the local values of the dielectric
function proximal to each other across the dielectrically homogeneous slab.
