Thermally driven magnetization switching of perpendicularly magnetized [Cu/Ni] multilayer/BaTiO3(100) heterostructures is demonstrated. While the magnetization of the multilayer shows the out-of-plane magnetic anisotropy in the tetragonal phase of BaTiO3 at room temperature, the magnetization orientation is found to switch from the out-of-plane to the in-plane in the rhombohedral phase below 180 K. The magnetization switching is attributed to the interfacial compressive strain transfer from BaTiO3 to [Cu/Ni] due to the structural phase transitions of BaTiO3. Magneto-optical polar Kerr measurement in the rhombohedral phase with and without applying an electric field supports the description that the magnetization switching arises from the compressive strain at the interface induced by the structural phase transition from the orthorhombic to rhombohedral phases.