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The microstructure evolution (crystallite size and microstrain) as well as the residual stress of Cu thin films of various thicknesses (250 nm, 500 nm, and 1 μm) on passivated Si substrates during isochronal annealing was investigated by in situ X-ray diffraction measurements in the temperature range between 25 °C and 250 °C. Before annealing, the thermoelastic behavior was investigated excluding the occurrence of thermally activated relaxation processes occurring above ambient temperature by in situ stress measurements below ambient temperature. On this basis, above ambient temperature, effects of stress relaxation and emerging secondary stresses (due to grain growth and annihilation of crystal defects, giving rise to a considerable tensile stress contribution development) could be identified for all three layers in the temperature regime between ambient temperature and 250 °C. Grain growth in the nanocrystalline thin films started at much lower temperatures as compared to coarse-grained materials. The results were discussed in terms of the effects of different driving forces and grain-boundary mobilities acting in nanocrystalline materials.