At present, 30–40 per cent of the baryons in the local Universe is still undetected. According to theoretical predictions, this gas should reside in filaments filling the large-scale structure (LSS) in the form of a warm–hot intergalactic medium (WHIM), at temperatures 105–107 K, thus emitting in the soft X-ray energies via free–free interaction and line emission from heavy elements. In this work, we characterize the properties of the X-ray emission of the WHIM, and the LSS in general, focusing on the influence of different physical mechanisms, namely galactic winds (GWs), black hole feedback and star formation, and providing estimates of possible observational constraints. To this purpose, we use a set of cosmological hydrodynamical simulations that include a self-consistent treatment of star formation and chemical enrichment of the intergalactic medium, which allows us to follow the evolution of different metal species. We construct a set of simulated light cones to make predictions of the emission in the 0.3–10 keV energy range. We obtain that GWs increase the emission of both galaxy clusters and WHIM by a factor of 2. The amount of oxygen at average temperature and, consequently, the amount of expected bright O vii and O viii lines are increased by a factor of 3 due to GWs and by 20 per cent when assuming a top-heavy initial mass function. We compare our results with current observational constraints and find that the emission from faint groups and WHIM should account for half to all of the unresolved X-ray background in the 1–2 keV band.