  The isotropy of the late Universe is an assumption greatly used in astronomy.
However, many studies have recently reported deviations from isotropy with a
definitive conclusion yet to be made. New, independent methods to robustly test
the cosmic isotropy are of crucial importance. In this work, we investigate the
directional behavior of the X-ray luminosity-temperature ($L_X-T$) relation of
galaxy clusters. A tight correlation exists between the luminosity and
temperature of the X-ray-emitting intracluster medium. While the measured
luminosity depends on the underlying cosmology, the temperature can be
determined without any cosmological assumptions. By exploiting this property
one can effectively test the isotropy of cosmological parameters over the full
extragalactic sky. Here, we used 313 homogeneously selected X-ray galaxy
clusters from the MCXC catalog and obtained core-excised temperatures for all
of them. We find that the behavior of the $L_X-T$ relation heavily depends on
the direction of the sky. Strong anisotropies are detected at a $\sim 4\sigma$
level toward $(l,b)\sim (280^{\circ}, -20^{\circ})$. Several X-ray and
cluster-related effects that could potentially explain these anisotropies were
examined, but none did so. Interestingly, two other available cluster samples
appear to have a similar behavior throughout the sky, while being fully
independent of each other and our sample. Performing a joint analysis of the
three samples, the final anisotropy is further intensified ($\sim 5\sigma$),
toward $(l,b)\sim (303^{\circ}, -27^{\circ})$, which is in good agreement with
other cosmological probes. This result demonstrates that X-ray galaxy cluster
studies that assume perfect isotropy can produce strongly biased results
whether the underlying reason is cosmological or related to X-rays. The
identification of the exact nature of these anisotropies is therefore crucial.
