We present a study of a recurring jet observed on October 31, 2011 by SDO/AIA, Hinode/XRT and Hinode/EIS. We discuss the physical parameters of the jet such as density, differential emission measure, peak temperature, velocity and filling factor obtained using imaging and spectroscopic observations. A differential emission measure (DEM) analysis was performed at the region of the jet-spire and the footpoint using EIS observations and also by combining AIA and XRT observations. The DEM curves were used to create synthetic spectra with the CHIANTI atomic database. The plasma along the line-of-sight in the jet-spire and jet-footpoint was found to be peak at 2.0 MK. We calculated electron densities using the Fe XII ($\lambda$186/$\lambda$195) line ratio in the region of the spire (Ne = 7.6x$1010$ $cm-3$) and the footpoint (1.1x$1011$ $cm-3$). The plane-of-sky velocity of the jet is found to be 524 km/s. The resulting EIS DEM values are in good agreement with those obtained from AIA-XRT. There is no indication of high temperatures, such as emission from Fe XVII ($\lambda$254.87)(logT[K]=6.75)seeninthejet-spire.Incaseofthejet-footpoint,syntheticspectrapredictweakcontributionsfromCaXVII($\lambda$192.85)andFeXVII($\lambda$254.87).Withfurtherinvestigation,weconfirmedemissionfromtheFeXVIII($\lambda$93.932) line in the AIA 94 $\backslash AA$ channel in the region of the footpoint. We also found good agreement between the estimated and predicted Fe XVIII count rates. A study of the temporal evolution of the jet-footpoint and the presence of high-temperature emission from the Fe XVIII (log T [K] = 6.85) line leads us to conclude that the hot component in the jet-footpoint was present initially that the jet had cooled down by the time EIS observed it.