Context : Aims : We explore the high spectral resolution X-ray data towards the quasar 3C 273 to search for signals of hot ( \sim 10 ^ { 6 - 7 } K ) X-ray-absorbing gas co-located with two established intergalactic FUV O VI absorbers . Methods : We analyze the soft X-ray band grating data of all XMM- Newton and Chandra instruments to search for the hot phase absorption lines at the FUV predicted redshifts . The viability of potential line detections is examined by adopting the constraints of a physically justified absorption model . The WHIM hypothesis is investigated with a complementary 3D galaxy distribution analysis and by detailed comparison of the measurement results to the WHIM properties in the EAGLE cosmological , hydrodynamical simulation . Results : At one of the examined FUV redshifts , z = 0.09017 \pm 0.00003 , we measured signals of two hot ion species , O VIII and Ne IX , with a 3.9 \sigma combined significance level . While the absorption signal is only marginally detected in individual co-added spectra , considering the line features in all instruments collectively and assuming collisional equilibrium for absorbing gas , we were able to constrain the temperature ( kT = 0.26 \pm 0.03 keV ) and the column density ( N _ { \mathrm { H } } \times \mathrm { Z _ { \sun } / Z } = 1.3 _ { -0.5 } ^ { +0.6 } \times 10 ^ { 19 } cm ^ { -2 } ) of the absorber . Thermal analysis indicates that FUV and X-ray absorption relate to different phases , with estimated temperatures , T _ { \mathrm { FUV } } \approx 3 \times 10 ^ { 5 } , and , T _ { \mathrm { X - ray } } \approx 3 \times 10 ^ { 6 } K. These temperatures match the EAGLE predictions for WHIM at the FUV/X-ray measured N _ { \mathrm { ion } } -ranges . We detected a large scale galactic filament crossing the sight-line at the redshift of the absorption , linking the absorption to this structure . Conclusions : This study provides observational insights into co-existing warm and hot gas within a WHIM filament and estimates the ratio of the hot and warm phases . Because the hot phase is thermally distinct from the O VI gas , the estimated baryon content of the absorber is increased , conveying the promise of X-ray follow-up studies of FUV detected WHIM in refining the picture of the missing baryons .