  The fraction of ionized gas in the Warm Hot Intergalactic Medium induces
temperature anisotropies on the Cosmic Microwave Background similar to those of
clusters of galaxies. The Sunyaev-Zel'dovich anisotropies due to these low
density, weakly non-linear, baryon filaments can not be distinguished from that
of clusters using frequency information, but they can be separated since their
angular scales are very different. To determine the relative contribution of
the WHIM SZ signal to the radiation power spectrum of temperature anisotropies,
we explore the parameter space of the concordance LCDM model using Monte Carlo
Markov Chains and the Wilkinson Microwave Anisotropy Probe 7yr and South Pole
Telescope data. We find marginal evidence of a contribution by diffuse gas,
with amplitudes of A_WHIM=10-20 muK^2, but the results are also compatible with
a null contribution from the WHIM, allowing to set an upper limit of A_WHIM <
43 muK^2 (95.4% C.L.). The signal produced by galaxy clusters remains at
A_CL=4.5 muK^2, a value similar to what is obtained when no WHIM is included.
From the measured WHIM amplitude we constrain the temperature-density phase
diagram of the diffuse gas, and find it to be compatible with numerical
simulations. The corresponding baryon fraction in the WHIM varies from 0.43 to
0.47, depending on model parameters. Planck data could set tighter constraints
on the temperature-density relation.
