We report on the structure and evolution of a current sheet that formed in the wake of an eruptive X8.3 flare observed at the west limb of the Sun on 2017 September 10. Using observations from the EUV Imaging Spectrometer (EIS) on Hinode and the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory, we find that plasma in the current sheet reaches temperatures of about 20 MK and that the range of temperatures is relatively narrow. The highest temperatures occur at the base of the current sheet, in the region near the top of the post-flare loop arcade. The broadest high temperature line profiles, in contrast, occur at the largest observed heights. Furthermore, line broadening is strong very early in the flare and diminishes over time. The current sheet can be observed in the AIA 211 and 171 channels, which have a considerable contribution from thermal bremsstrahlung at flare temperatures. Comparisons of the emission measure in these channels with other EIS wavelengths and AIA channels dominated by Fe line emission indicate a coronal composition and suggest that the current sheet is formed by the heating of plasma already in the corona. Taken together, these observations suggest that some flare heating occurs in the current sheet, while additional energy is released as newly reconnected field lines relax and become more dipolar.