The process of high-speed energy transfer in media with allowance for the effects of the internal structure is considered in the context of nonequilibrium statistical mechanics and the theory of nonlinear operator systems. The self-consistent nonlocal-hydrodynamic approach proposed enables one to introduce multiple scales and multiple stages of the processes of exchange of momentum and energy into the continuous description of a medium. Large-scale fluctuations transferring heat in a wave manner are generated in the medium at the initial stage of rapid heating. The measurable characteristic of these fluctuations, i.e., the dispersion of mass velocity, has been introduced into the nonequilibrium equations of state of the medium. The mechanism of regular heat conduction is established in the medium at the final stage of the process, and a synergetic formation of new structures occurs in the interval.