Blends of Cu powders and 3 vol. % carbon nanotubes (CNTs), and an additional sample from pure Cu powder were consolidated by High Pressure Torsion (HPT) at room temperature (RT) and 373 K. The grain size, the lattice defect densities as well as the hardness of the pure and composite materials were determined. Due to the pinning effect of CNTs, the dislocation density is about three times larger, while the grain size is about half of that obtained in the sample consolidated from the pure Cu powder. The increase of the HPT-processing temperature from RT to 373 K resulted in only a slight increase of the grain size in the Cu-CNT composite while the dislocation density and the twin boundary frequency were reduced significantly. The flow stress obtained experimentally agrees well with the value calculated by the Taylor-formula indicating that the strength in both pure Cu and Cu-CNT composites is determined mainly by the interaction between dislocations. The addition of CNTs to Cu yields a significantly better thermal stability of the UFG matrix processed by HPT.