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Results are presented for our search for warm-hot gas towards the quasar Q0329-385. We identify ten OVI systems of which two are within 5000 km/s of z_emand a third one should be of intrinsic origin. The seven remaining systems haveHI column densities 10^13.7<N(HI)<10^15.6 cm^-2. At least ~1/3 of theindividual OVI sub-systems have temperatures T<1x10^5 K and cannot originate incollisionally ionized gas. Photoionization by a hard UV background fieldreproduces well the ionic ratios for metallicities in the range 10^-2.5 -10^-0.5 solar, with possibly sub-solar N/C relative abundance. For [O/C]=0, thesizes inferred for the OVI clouds are in some cases larger than the maximumextent implied by the Hubble flow. This constraint is fulfilled assuming amoderate overabundance of oxygen relative to carbon. For a soft UV ionizingspectrum, an overabundance of O/C is required, [O/C]~0.0-1.3. For a hard(soft)UV spectrum and [O/C]=0(1), the OVI regions have overdensities in 10-40.Comment: accepted by A&A Letters, 5 pages, 6 figure

The warm-hot intergalactic medium at $\mathsf{\vec {z}\sim2.2}$: Metal enrichment and ionization source