  The evolution with redshift of the temperature-luminosity relation of X-ray
galaxy clusters is a key ingredient to break degeneracies in the interpretation
of X-ray clusters redshift number counts. We therefore take advantage of the
recent measurements of the temperature-luminosity relation of distant clusters
observed with XMM-Newton and Chandra satellites to examine theoretical number
counts expected for different available X-rays cluster samples, namely the
RDCS, EMSS, SHARC, 160deg^2 and the MACS at redshift greater than 0.3. We
derive these counts without any adjustment, using models previously normalized
to the local temperature distribution function and to the high-z (z = 0.33)
TDF. We find that these models having Omega_M in the range [0.85-1.] predict
counts in remarkable agreement with the observed counts in the different
samples. We illustrate that this conclusion is weakly sensitive to the various
ingredients of the modeling. Therefore number counts provide a robust evidence
of an evolving population. A realistic flat low density model (Omega_M = 0.3),
normalized to the local abundance of clusters is found to overproduce cluster
abundance at high redshift (above z = 0.5) by nearly an order of magnitude.
This result is in conflict with the popular concordance model. The conflict
could indicate a deviation from the expected scaling of the M-T relation with
redshift.
