The cosmological missing baryons at z<1 most likely hide in the hot (T K) phase of the Warm Hot Intergalactic Medium (WHIM). While the hot WHIM is hard to detect due to its high ionisation level, the warm (T K) phase of the WHIM has been very robustly detected in the FUV band. We adopted the assumption that the hot and warm WHIM phases are co-located and thus used the FUV-detected warm WHIM as a tracer for the cosmologically interesting hot WHIM. We utilised the assumption by performing an X-ray follow-up in the sight line of a blazar PKS 2155-304 at the redshifts where previous FUV measurements of OVI, SiIV and BLA absorption have indicated the existence of the warm WHIM. We looked for the OVII He and OVIII Ly absorption lines, the most likely hot WHIM tracers. Despite of the very large exposure time ( 1 Ms), the XMM-Newton/RGS1 data yielded no significant detection which corresponds to upper limits of $\log{N({\rm OVII})({\rm cm}^{-2}))} \le 14.5-15.2\log{N({\rm OVIII})({\rm cm}^{-2}))} \le 14.9-15.2$. An analysis of LETG/HRC data yielded consistent results. However, the LETG/ACIS data yielded a detection of an absorption line

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