In the local universe, a large fraction of the baryon content is believed to exist as diffuse gas in filaments. While this gas is directly observable in X-ray emission around clusters of galaxies, it is primarily studied through its UV absorption. Recently, X-ray observations of large-scale filaments connecting to the cosmic web around the nearby (z = 0.05584) cluster A133 were reported. One of these filaments is intersected by the sightline to quasar VV98 J010250.2−220929, allowing for a first-ever census of cold, cool, and warm gas in a filament of the cosmic web where hot gas has been seen in X-ray emission. Here, we present UV observations with the Cosmic Origins Spectrograph and optical observations with the Magellan Echellette spectrograph of VV98 J010250.2−220929. We find no evidence of cold, cool, or warm gas associated with the filament. In particular, we set a 2 upper limit on Ly absorption of log(NH i/cm−2) < 13.7, assuming a Doppler parameter of b = 20 km s−1. As this sightline is ∼1100 pkpc (0.7Rvir) from the center of A133, we suggest that all gas in the filament is hot at this location, or that any warm, cool, or cold components are small and clumpy. A broader census of this system-combining more UV sightlines, deeper X-ray observations, and a larger redshift catalog of cluster members-is needed to better understand the roles of filaments around clusters.