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We discuss mesons in thermalizing gluon backgrounds in the N=2 supersymmetric QCD using the gravity dual. We numerically compute the dynamics of a probe D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background thermalizing from zero to finite temperatures by energy injection. In static backgrounds, it has been known that there are two kinds of brane embeddings where the brane intersects the black hole or not. They correspond to the phases with melted or stable mesons. In our dynamical setup, we obtain three cases depending on final temperatures and injection time scales. The brane stays outside of the black hole horizon when the final temperature is low, while it intersects the horizon and settles down to the static equilibrium state when the final temperature is high. Between these two cases, we find the overeager case where the brane dynamically intersects the horizon although the final temperature is not high enough for a static brane to intersect the horizon. The interpretation of this phenomenon in the dual field theory is meson melting due to non-thermal effects caused by rapid energy injection. In addition, we comment on the late time evolution of the brane and a possibility of its reconnection.
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