Point-contact spectroscopy is a powerful tool for probing superconductors. One of the most common observations in the point-contact spectra on the recently discovered ferropnictide superconductors is a large conductance asymmetry with respect to voltage across the point-contact. In this paper we show that the antisymmetric part of the point-contact spectrum between a silver tip and an epitaxial thin film of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ shows certain unique features. These features have an interesting evolution with increasing temperature up to a temperature that is 30% larger than the critical temperature $T_c$ of the superconductor. We argue that this evolution can be associated with the rich normal state properties of these materials.
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