A complete phenomenological model of the two-temperature plasma with developed (strong) turbulence is proposed and investigated. The model is suitable for the simulation of the physical processes occurring in the plasmas of fast classical (Z-) and screw (S-) pinches at the stagnation stage. The notion of the turbulent-thermal entropy is introduced for plasmas with strong turbulence and a dynamic equation describing the evolution of the plasma in space and time is derived. The equations of state proposed allow one to determine unambiguously the thermodynamic functions and transport coefficients for a plasma with strong large-scale turbulence. Peculiarities of the establishment of thermodynamic equilibrium in a two-temperature plasma with strong large-scale turbulence are discussed.