[en] We present new measurements of the time variability of intensity, Doppler, and nonthermal velocities in moss in an active region core observed by the EUV Imaging Spectrometer on Hinode in 2007 June. The measurements are derived from spectral profiles of the Fe XII 195 A line. Using the 2'' slit, we repeatedly scanned 150'' by 150'' in a few minutes. This is the first time it has been possible to make such velocity measurements in the moss, and the data presented are the highest cadence spatially resolved maps of moss Doppler and nonthermal velocities ever obtained in the corona. The observed region produced numerous C- and M-class flares with several occurring in the core close to the moss. The magnetic field was therefore clearly changing in the active region core, so we ought to be able to detect dynamic signatures in the moss if they exist. Our measurements of moss intensities agree with previous studies in that a less than 15% variability is seen over a period of 16 hr. Our new measurements of Doppler and nonthermal velocities reveal no strong flows or motions in the moss, nor any significant variability in these quantities. The results confirm that moss at the bases of high temperature coronal loops is heated quasi-steadily. They also show that quasi-steady heating can contribute significantly even in the core of a flare productive active region. Such heating may be impulsive at high frequency, but if so it does not give rise to large flows or motions.