We will present Infrared Space Observatory (ISO) measurements of the far-infrared (FIR) fine structure lines [SIV] (10.5 micron), [SIII], (33.5 micron), [OIII] (51.8, 88.4 micron), [NIII] (57.3 micron), [NII] (121.9 micron), [OI] (63.2, 145.5 micron), and [CII] (157.7 micron) at five positions on the thermal ("Arched") Filaments in the Galactic Center. Both Long Wavelength Spectrometer (LWS) and Short Wavelength Spectrometer (SWS) observations were taken to investigate the impact on the interstellar medium of the massive young "Arches" cluster. The observed positions were selected to provide measurements at uniformly increasing distances from the Arches Cluster. The diagnostic line ratios most sensitive to ionizing temperature decrease with distance from the cluster, providing strong evidence that the cluster is the only ionization source for the Arched Filaments. The total FIR luminosity peaks on the filament closest to the cluster and also decreases uniformly with distance from the cluster.