Several popular cosmological models predict that most of the baryonic mass in the local universe is located in filamentary and sheet-like structures associated with galaxy overdensities. This gas is expected to be gravitationally heated to ~106 K and therefore emitting in the soft X-rays. We have detected diffuse soft X-ray structures in a high Galactic latitude ROSAT field after point source subtraction and correction for Galactic absorption. These diffuse structures have an X-ray energy distribution that is much softer than expected from clusters, groups or unresolved emission from AGNs, but are consistent with that expected from a diffuse warm intergalactic medium. To discriminate between a Galactic or extragalactic nature of the diffuse gas we have correlated the soft X–map with multiband optical images in this field. We have found a significant overdensity of galaxies in correspondence with the strongest diffuse X-ray structure. The photometric redshift distribution of the galaxies over the X-ray peak has an excess over field galaxies at . This result strongly suggests that the diffuse X-ray flux is due to extragalactic emission by warm gas associated with an overdense galaxy region at .