Based on the Krylov-Bogolyubov method of averaging the closed system of equations for particle motion and temperature in inhomogeneous rapidly oscillating velocity and temperature of fluid phase is derived. It is shown that the particle movement in a rapidly oscillating fluid velocity field occurs not only under the force of gravity and resistance, but also under force of migration. The migration force is the result of particle inertia and in homogeneity of oscillation of velocity field of the carrier phase. Effects of dynamic and thermal relaxation times of particle and gravity force have been studied. It is shown possibilities of accumulation of particles under the combined action of gravity and migration forces. For a linear dependence of the amplitude of velocity and temperature fluctuations of the fluid an analytical solution was presented. The analytical solutions have been found in good agreement with the results of numerical solution of system of equations of motion and heat transfer of particle.