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Abstract. The X-ray background intensity around Lick count galaxies and rich clusters of galaxies is investigated in three ROSAT energy bands. It is found that the X-ray enhancements surrounding concentrations of galaxies exhibit significantly softer spectrum than the standard cluster emission and the average extragalactic background. The diffuse soft emission accompanying the galaxies is consistent with the thermal emission of the hot gas postulated first by the Cen & Ostriker hydrodynamic simulations. Our estimates of the gas temperature -although subject to large uncertainties -averaged over several Mpc scales are below 1 keV, which is substantially below the temperature of the intra-cluster gas, but consistent with temperatures predicted for the local intergalactic medium. It is pointed out that the planned ROSITA mission would be essential for our understanding of the diffuse thermal component of the background.