Magnetic films with perpendicular magnetic anisotropy (PMA) are the basis for efficient memory-storage and future spintronic devices. PMA predominantly stems from surface effects, e.g., symmetry reduction, at the magnetic-layer interface and quickly decays with increasing layer thickness. Strong PMA is thus typically observed in sub-nanometer multilayers with alternating magnetic and noble metals. Using in-situ temperature-dependent measurements of ferromagnetic resonance it is demonstrated that strong PMA can be achieved in Si/Ni multilayers with individual layer as thick as 16 nm. Here, PMA is imposed by thermal strains acting via magnetoelastic coupling and directly depends on the annealing temperature and time, which regulate the diffusion-driven plastic deformation. This opens a way to PMA-film fabrication that avoids complex and resource-intensive production of atomically thin multilayers.