Conventional glow plasma was engaged to study the effect induced by change of temperature controlled by a corresponding change of the discharge power, with relation to the fabrication of 2D and 3D CuO nanostructures. It was shown, that at the same oxygen pressure of 465 Pa, 2D nanostructures are synthesized on a surface of copper samples, with the tendency to form loosely-packed cabbage-like and tree-like 3D nanostructures, when the temperature of the samples is maintained in the range of 820–850 ℃. At the same time, much more stacked 3D nanostructures, with densely-packed cabbage-like architecture are grown at the temperatures of 860–900 ℃. It was demonstrated that heat transfer from the samples treated in the discharge is approximated well by the assumption of radiant heat exchange described by the Stefan-Boltzmann law, which greatly facilitate forecasting of the treatment results in future studies. A comparison of the temperature increase rates during the heating of the samples in the plasma-enhanced process, with the typical values obtained for thermal synthesis, allowed to conclude about the leading role of internal stresses that are generated in the layer of copper oxide. Both the increase rate of the temperature and temperature itself are responsible for the transition of 2D to 3D nanostructures observed in the conducted experiment. The results are important with relation to the development of a robust and efficient technology of fabrication of copper oxide nanostructures of different morphology.