A semi-infinite laminated composite is considered in which the matrix and filler material are aligned parallel to the heat propagation direction. The face x = 0 of the composite is subject to a heat input which has frequency ω, and spacewise it has y-periodicity conforming to the periodicity of the layered composite. The rigorous solution for the temperature distribution in the composite is presented, when a sinusoidal boundary flux (or temperature) is imposed on the free surface. As a representative example a nickel matrix and aluminum filler composite is considered. The ensuing temperature distribution throughout the composite is illustrated for a low-frequency as well as a high-frequency heat flux boundary condition. The existence of a "thermal shock layer" at the interface, across which the temperature jumps, almost discontinuously, is exhibited.