  The correlation of weak lensing and Cosmic Microwave Anisotropy (CMB) data
traces the pressure distribution of the hot, ionized gas and the underlying
matter density field. The measured correlation is dominated by baryons residing
in halos. Detecting the contribution from unbound gas by measuring the residual
cross-correlation after masking all known halos requires a theoretical
understanding of this correlation and its dependence with model parameters. Our
model assumes that the gas in filaments is well described by a log-normal
probability distribution function, with temperatures $10^{5-7}$K and
overdensities $\xi\le 100$. The lensing-comptonization cross-correlation is
dominated by gas with overdensities in the range $\xi\approx[3-33]$; the signal
is generated at redshifts $z\le 1$. If only 10\% of the measured
cross-correlation is due to unbound gas, then the most recent measurements set
an upper limit of $\bar{T}_e\lesssim 10^6$K on the mean temperature of Inter
Galactic Medium. The amplitude is proportional to the baryon fraction stored in
filaments. The lensing-comptonization power spectrum peaks at a different scale
than the gas in halos making it possible to distinguish both contributions. To
trace the distribution of the low density and low temperature plasma on
cosmological scales, the effect of halos will have to be subtracted from the
data, requiring observations with larger signal-to-noise ratio than currently
available.
