  At z<1 a large fraction of the baryons is thought to reside in diffuse gas
that has been shock-heated to high temperatures (log T=5-6). Absorption by the
770.41, 780.32 {\AA} doublet of NeVIII in quasar spectra represents a unique
tool to study this elusive warm-hot phase. We have developed an analytic model
for the properties of NeVIII absorbers that allows for an inhomogeneous metal
distribution. Our model agrees with the predictions of a simulation from the
OWLS project indicating that the average line-of-sight metal-filling fraction
within the absorbing gas is low (c_L~0.1). Most of the NeVIII in our model is
produced in low-density, collisionally ionized gas (log n=-6 to -4 cm^-3, log
T=5-6). Strong NeVIII absorbers (log N(NeVIII)>14), like those recently
detected by HST/COS, are found to arise in higher density gas (log n>-4, log
T=5.75). NeVIII cloudlets harbour only 1 per cent of the cosmic baryon budget.
The baryon content of the surrounding gas (which has similar densities and
temperatures as the NeVIII cloudlets) is a factor 1/c_L higher. We conclude
that NeVIII absorbers are robust probes of shock-heated diffuse gas, but that
spectra with signal-to-noise ratios S/N>100 would be required to detect the
bulk of the baryons in warm-hot gas.
