Two Co/Si/W/Si multilayers with 15 nm (ML1) and 19 nm (ML2) nominal periods were prepared by UHV electron beam evaporation onto Si(100) wafers. Except for Co layers in ML2, the layers were amorphous after deposition. The evolution of multilayer stack and interface behaviour on rapid thermal annealing (RTA) were studied by specular X-ray reflectivity and grazing incidence diffuse scattering which were evaluated within Fresnel formalism and distorted-wave Born approximation, respectively. The thermal stability of both multilayers is governed by intermixing and interdiffusion starting at Co/Si interfaces and by silicide crystallization above 773 K. The lateral correlation length of the interfaces increases and their strong vertical correlation gets weaker and dependent on the interface roughness frequency with proceeding RTA. The layered structure collapses on the 1273K/30s RTA in ML1 which is by 250 K higher than for a W/Si multilayer. The interface behaviour is similar in ML2, however, the layered structure is heavily disturbed already on the 1023K/30s RTA due to a larger volume reduction at silicide crystallization and faster diffusion.