With the use of the EAGLE simulation, I present the spatial and thermal distribution of the baryons within the filaments of the Cosmic Web. In particular, I characterise the properties of the hottest (log T(K) > 5.5) Warm-Hot Intergalactic Medium (WHIM). As observations of the diffuse intergalactic medium at these temperatures are extremely challenging, the hot WHIM remains largely undetected and is a candidate to solve the cosmological missing baryon problem. Indeed, the EAGLE simulation predicts a large fraction of baryons to be in the hot WHIM. I demonstrate how we located the hot WHIM and examined its radial temperature and density profiles by using the Bisous and MMF/NEXUS+ filament finders, and show how the galaxy luminosity density can aid in selecting the most promising filaments for future observations.