We present a numerical scheme to study the dynamics of slow light and light storage in an electromagneticallyinduced- transparency (EIT) medium at finite temperatures. Allowing for the motional coupling, we derive a set of coupled Schr{o}dinger equations describing a boosted closed three-level EIT system according to the principle of Galilean relativity. The dynamics of a uniformly moving EIT medium can thus be determined by numerically integrating the coupled Schrodinger equations for atoms plus one ancillary Maxwell-Schrodinger equation for the probe pulse. The central idea of this work rests on the assumption that the loss of ground-state coherence at finite temperatures can be ascribed to the incoherent superposition of density matrices representing the EIT systems with various velocities. Close agreements are demonstrated in comparing the numerical results with the experimental data for both slow light and light storage. In particular, the distinct characters featuring the decay of ground-state coherence can be well verified for slow light and light storage. This warrants that the current scheme can be applied to determine the decaying profile of the ground-state coherence as well as the temperature of the EIT medium.
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