Cu/AlN-Al2O3 nano-multilayer (NML) was deposited by magnetron sputtering method on 42CrMo4 steel samples, starting with a 15 nm AlN-Al2O3 layer and followed by 200 alternating layers of 5 nm thick Cu and 5 nm thick AlN-Al2O3 layers. The microstructure and thermal behaviour of the as-deposited and heat-treated multilayer was studied. Starting from about 400 degrees C, extensive coarsening of Cu nanocrystallites and the migration of Cu within the multilayer were observed via solid-state diffusion. Part of the initial Cu even formed micron-sized reservoirs within the NML. Due to increased temperature and to the different heat expansion coefficients of Cu and the AlN-Al2O3, the latter cracked and Cu appeared on the top surface of the NML at around 250 degrees C. Below 900 degrees C, the transport of Cu to the top surface of the NML probably took place as a solid-state flow, leading to faceted copper micro-crystals. However, above 900 degrees C, the Cu micro-crystals found on the top of the NML have rounded shape, so they were probably formed by pre-melting of nano-layered Cu due to its high specific surface area in the NML. Even if the Cu crystals appear on the top surface of the NML via solid-state flow without pre-melting, the Cu crystals on the top surface of the NML can be potentially used in joining applications at and above 250 degrees C.