Heat conduction of a suspension subjected to a time-dependent spatially constant temperature gradient is studied with the aid of stochastic functional expansions with random-point basis functions. It is argued that the basis function which is appropriate for modelling the chaotic behavior of nonlinear dynamical systems, e.g., turbulence, is not suited for studying the composite materials. It is shown that within the first order of approximation with respect to the concentration, the equation for the kernel of the 1st-order functional integral is the equation of the disturbance introduced by a single sphere (filler) in a matrix subjected to a time-dependent temperature gradient. After solving the resulting initial-boundary value problem, the effective correlation between the heat flux and temperature gradient is established. It turns out that the effective law involves a retardation (memory integral) of the temperature gradient. Approximate expression for the memory kernel is found by employing a method based on infinite series expansion. An interesting limiting case of filler material with infinite conductivity is discussed where memory integral becomes the Riemann-Liouville half integral.