example, two direct probes of the AGN-activity history are $(i)$ the entropy profile of local and [*high-z*]{} objects [@dubois.etal.2011; @chaudhuri.etal.2012; @ettori.etal.2013; @pointecouteau.etal.2013] and $(ii)$ the relation between the clusters X-ray luminosity and their temperature and its evolution [@2012MNRAS.424.2086H; @takey.etal.2013; @2015arXiv151203833G]. To decode such important measurements and to extend high-redshift studies of galaxy clusters, the X-ray community is planning and working on future missions such as e-ROSITA[^1][@2012arXiv1209.3114M] and Athena[^2] [@nandra.etal.2013]. These will be complementary to millimetric surveys, e.g. SPT-G3 [@benson.etal.2014], or optical ones, e.g. EUCLID[^3] [@laureijs.etal.2011] or LSST[^4][@Ivezic.etal.2008]. Both X-ray missions will build copious samples of clusters and groups of galaxies at $z \sim 1$ or above to advance high-z investigations that are currently limited mostly to $z \leq 0.7$ objects with sparse data from most distant times (). The simplest approach to measure the mass of a large sample of objects is to access to [*scaling relations*]{} between the total mass and some observable quantities that are easier to derive. In X-rays studies, the most common mass-proxies are the [*gas mass*]{}, $M_{\rm gas}$, which can be extracted from the surface brightness profile, the [*temperature*]{}, $T$, which is solidly estimated from X-ray spectra with, at least, one thousand of counts, and 