  X-ray emission from the distant lensing cluster CL2236-04 at $z$ = 0.552 was
discovered by ASCA and ROSAT/HRI observations. If the spherical symmetric mass
distribution model of the cluster is assumed, the lensing estimate of the
cluster mass is a factor of two higher than that obtained from X-ray
observations as reported for many distant clusters. However, the elliptical and
clumpy lens model proposed by Kneib et al.(1993) is surprisingly consistent
with the X-ray observations assuming that the X-ray emitting hot gas is
isothermal and in a hydrostatic equilibrium state. The existence of the cooling
flow in the central region of the cluster is indicated by the short central
cooling time and the excess flux detected by ROSAT/HRI compared to the ASCA
flux. However, it is shown that even if the AXJ2239-0429 has a cooling flow in
the central region, the temperature measured by ASCA which is the mean
emission-weighted cluster temperature in this case, should not be cooler than
and different from the virial temperature of the cluster. Therefore, we
conclude that the effect of the clumpiness and non-zero ellipticity in the mass
distribution of the cluster are essential to explain the observed feature of
the giant luminous arc, and there is no discrepancy between strong lensing and
X-ray estimation of the mass of the cluster in this cluster.
