The hypothesis of "independent averaging" suggested by Corrsin [J. Atmos. Sci. 20 (1963) 115] is generalized for investigating the influence of turbulent microstructure on the intensity of velocity and temperature fluctuations of inertial particles. It has been shown that parameters of turbulent motion and heat transfer in a dispersed phase also depend on dynamic and thermal relaxation times of particles. It is established that amplitudes of velocity and temperature fluctuations of the dispersed phase are expressed in terms of the Eulerian space-time correlation functions measured in the system of coordinates moving with mean velocity of fluid flow. Association between Lagrangian and Eulerian turbulent time macroscales of various types of flows was estimated. These parameters were evaluated on the basis of published experimental data.