  The role played by the intergalactic medium (IGM) in the X-ray absorption
towards high-redshift sources has recently drawn more attention in spectral
analysis studies. Here, we study the X-ray absorption towards 15 flat-spectrum
radio quasars at $z>2$, relying on high counting statistic ($\gtrsim10\,000$
photons) provided by XMM-Newton, with additional NuSTAR (and simultaneous
Swift-XRT) observations when available. Blazars can be confidently considered
to have negligible X-ray absorption along the line of sight within the host
galaxy, likely swept by the kpc-scale relativistic jet. This makes our sources
ideal for testing the absorption component along the IGM. Our new approach is
to revisit the origin of the soft X-ray spectral hardening observed in high-z
blazars in terms of X-ray absorption occurring along the IGM, with the help of
a low-z sample used as comparison. We verify that the presence of absorption in
excess of the Galactic value is the preferred explanation to explain the
observed hardening, while intrinsic energy breaks, predicted by blazars'
emission models, can easily occur out of the observing energy band in most
sources. First, we perform an indirect analysis comparing the inferred amount
of absorption in excess of the Galactic value with a simulated IGM absorption
contribution, that increases with redshift and includes both a minimum
component from diffuse IGM metals, and the additional contribution of discrete
denser intervening regions. Then, we directly investigate the warm-hot IGM with
a spectral model on the best candidates of our sample, obtaining an average IGM
density of $n_0=1.01^{+0.53}_{-0.72}\times10^{-7}$ cm$^{-3}$ and temperature of
$\log(T/\text{K})=6.45^{+0.51}_{-2.12}$. A more dedicated study is currently
beyond reach, but our results can be used as a stepping stone for future more
accurate analysis, involving Athena.
