Significant evidence of ionosphere disturbance in connection to intense seismic events have been detected since two decades. It is generally believed that the energy transfer can be due to Acoustic Gravity Waves (AGW) excited at ground level by the earthquakes. In spite of the statistical evidence of the detected perturbations, the coupling between lithosphere and atmosphere has not been so far properly explained by an accurate enough model. In this paper, for the first time, we show the result of an analytical-quantitative model that describes how the pressure and density disturbance is generated in the lower atmosphere by the ground motion associated to earthquakes. The direct comparison between observed and modelled vertical profiles of the atmospheric temperature shows the capability of the model to accurately reproduce, with an high statistical significance, the observed temperature fluctuations induced by strong earthquakes.