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Galaxy clusters are the largest virialized objects in the universe. Their merger dynamics and their interactions with the cosmic filaments that connect them are important for our understanding of the formation of large-scale structure. In addition, cosmic filaments are thought to possess the missing baryons in the universe. Studying the interaction of galaxy clusters and filaments therefore has the potential to unveil the the origin of the baryons and the physical processes that occur during merger stages of galaxy clusters. In this paper, we study the connection between A3395 and the intercluster filament with NuSTAR, XMM-Newton, and Suzaku data. Since the NuSTAR observation is moderately contaminated by scattered light, we present a novel technique developed for disentangling this background from the emission from the intracluster medium. We find that the interface of the cluster and the intercluster filament connecting A3395 and A3391 does not show any signs of heated plasma, as was previously thought. This interface has low temperature, high density, and low entropy, thus we suggest that the gas is cooling, being enhanced by the turbulent or tidal 'weather' driven during the early stage of the merger. Furthermore, our temperature results from the NuSTAR data are in agreement with those from XMM-Newton, and from joint NuSTAR and XMM-Newton analysis for a region with ~25% scattered light contamination within 1 sigma. We show that the temperature constraint of the intracluster medium is valid even when the data are contaminated up to ~25% for ~5 keV cluster emission., Comment: 22 pages, 13 figures, 7 tables. Accepted for publication by ApJ