We have identified a large-scale structure traced by galaxies at z=0.8, within the Lockman Hole, by means of multi-object spectroscopic observations. By using deep XMM images we have investigated the soft X-ray emission from the Warm-Hot Intergalactic Medium (WHIM) expected to be associated with this large-scale structure and we set a tight upper limit to its flux in the very soft 0.2-0.4 keV band. The non-detection requires the WHIM at these redshifts to be cooler than 0.1 keV. Combined with the WHIM emission detections at lower redshift, our result indicates that the WHIM temperature is rapidly decreasing with redshift, as expected in popular cosmological models.
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