The warm-hot intergalactic medium (WHIM) contains a significant portion of the 'missing baryons'. Its detection in emission remains a challenge. Integral field spectrometers like X-IFU on board of the Athena satellite will secure WHIM detection in absorption and emission and, for the first time, allow us to investigate its physical properties. In our research, we use the CAMELS simulations to model the surface brightness maps of the OVII and OVIII ion lines and compute summary statistics like photon counts and 2-point correlation functions to infer the properties of the WHIM. Our findings confirm that detectable WHIM emission is primarily associated with galaxy haloes, and the properties of the WHIM show minimal evolution from z similar to 0.5 to the present time. By exploring a wide range of parameters within the CAMELS suite, we investigate the sensitivity of WHIM properties to cosmology and energy feedback mechanisms influenced by active galactic nuclei and stellar activity. This approach allows us to separate the cosmological aspects from the baryonic processes and place constraints on the latter. Additionally, we provide forecasts for WHIM observations using a spectrometer similar to X-IFU. We anticipate detecting 1-3 WHIM emission lines per pixel and mapping the WHIM emission profile around haloes up to a few tens of arcminutes, surpassing the typical size of a WHIM emitter. Overall, our work demonstrates the potential of emission studies to probe the densest phase of the WHIM, shedding light on its physical properties and offering insights into the cosmological and baryonic processes at play.
