  We assess the possibility to detect and characterize the physical state of
the missing baryons at low redshift by analyzing the X-ray absorption spectra
of the Gamma Ray Burst [GRB] afterglows, measured by a micro calorimeters-based
detector with 3 eV resolution and 1000 cm2 effective area and capable of fast
re-pointing, similar to that on board of the recently proposed X-ray satellites
EDGE and XENIA. For this purpose we have analyzed mock absorption spectra
extracted from different hydrodynamical simulations used to model the
properties of the Warm Hot Intergalactic Medium [WHIM]. These models predict
the correct abundance of OVI absorption lines observed in UV and satisfy
current X-ray constraints. According to these models space missions like EDGE
and XENIA should be able to detect about 60 WHIM absorbers per year through the
OVII line. About 45 % of these have at least two more detectable lines in
addition to OVII that can be used to determine the density and the temperature
of the gas. Systematic errors in the estimates of the gas density and
temperature can be corrected for in a robust, largely model-independent
fashion. The analysis of the GRB absorption spectra collected in three years
would also allow to measure the cosmic mass density of the WHIM with about 15 %
accuracy, although this estimate depends on the WHIM model. Our results suggest
that GRBs represent a valid, if not preferable, alternative to Active Galactic
Nuclei to study the WHIM in absorption. The analysis of the absorption spectra
nicely complements the study of the WHIM in emission that the spectrometer
proposed for EDGE and XENIA would be able to carry out thanks to its high
sensitivity and large field of view.
