We explore the high spectral resolution X-ray data towards the quasar 3C273 to search for signals of hot ($sim10^{6-7}$ K) X-ray-absorbing gas co-located with two established intergalactic FUV OVI absorbers. 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 comparison of the measurement results to the WHIM properties in the EAGLE cosmological, hydrodynamical simulation. At FUV redshift z=0.09017, we measured signals of two hot ion species, OVIII and NeIX, with a $3.9sigma$ combined significance level. Considering the line features in all instruments collectively and assuming collisional equilibrium for absorbing gas, we were able to constrain the temperature ($kT=0.26pm0.03$ keV) and the column density ($N_Htimes{Z_odot/Z}=1.3_{-0.5}^{+0.6}times10^{19}$ cm$^{-2}$) of the absorber. Thermal analysis indicates that FUV and X-ray absorption relate to different phases, with estimated temperatures $T_{FUV}approx3times10^5$ and $T_{X-ray}approx3times10^6$ K, which match the EAGLE predictions for WHIM at the FUV/X-ray measured $N_{ion}$-ranges. We detected a large scale galactic filament crossing the sightline at the redshift of the absorption, linking the absorption to this structure. This study provides 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 OVI 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.
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