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In the presence of perturbations of the thermospheric auroral region produced by traveling ionospheric disturbances during the propagation of atmospheric gravity waves, an analytical expression of the velocity of the thermospheric plasma is derived through magnetohydrodynamic formalism. The expressions of the Joule heating and the viscous heating are derived, and their rates of variation are presented. A threshold height for their transition has been determined from their ratio, which is in agreement with the experimental data. The analysis indicates that the time taken by the thermospheric plasma to reach a steady-state corresponds to the nature of the traveling ionospheric disturbances in the medium.