Based on observations from the Interface Region Imaging Spectrograph and Hinode, we analyze the thermodynamic evolution of the supra-arcade fan (SAF) in the 2017 September 10 flare. The SAF presents discontinuous characters during the rising process, indicating a nonuniform process of magnetic reconnection in the solar eruption. The intensity peaks of the high-temperature spectral lines (Fe xxi 1354.08 angstrom, Fe xxiii 263.76 angstrom, and Fe xxiv 255.10 angstrom) basically correspond to the valley of the Doppler velocity and Doppler width. The temperature and density increase spatially at the upper boundary of the SAF. These results indicate that a compressed interface may exist in the SAF, where the plasma environment shows remarkable changes in density, temperature, and turbulence. In view of the fact that the height of the SAF is close to the hard X-ray source, we conclude that the interface could be related to termination shocks (TSs), taking into account the synthetic spectral profiles obtained from numerical experiments. In turn, the variations of the spectral profiles might be useful tools for identifying TSs from EUV spectral observations.