We have theoretically investigated the in-plane lattice thermal conductivity of a quantum-dot superlattice. The calculations were carried out for a structure that consists of multiple layers of Si with randomly distributed Ge quantum dots separated by wetting layers and spacers. Our model takes into account scattering of acoustic phonons on spherical quantum dots, and corresponding modification of the phonon dispersion relation. The finite acoustic mismatch between Si and Ge is also taken into account. The obtained results are important for the most recently suggested applications of SiGe quantum-dot superlattices for thermoelectric devices.