Abstract The energy spectrum of cosmic rays exhibits power-like behavior with a very characteristic ‘knee’ structure. We consider a possibility that such a spectrum could be generated by some specific nonstatistical temperature fluctuations in the source of cosmic rays with the ‘knee’ structure reflecting an abrupt change of the pattern of such fluctuations. This would result in a generalized nonextensive statistical model for the production of cosmic rays. The possible physical mechanisms leading to these effects are discussed together with the resulting chemical composition of the cosmic rays, which follows the experimentally observed abundance of nuclei.