  RX J1131-1231 is a gravitationally lensed system which includes four images
of a quasar lensed by an elliptical galaxy. The flux in the individual images
is known to be affected by microlensing effect in the visible and X-ray bands.
We study the multi-wavelength properties of RX J1131-1231 over a broad energy
range, from optical to hard X-ray, during the periods of the microlensing
caustic crossings. We aim to constrain the spatial extent of the X-ray emission
region at different energies. We combine the data of the source monitoring in
the visible band with the X-ray data of the Burst Alert Telescope (BAT) on
board of SWIFT satellite and Chandra X-ray observatory. Inspecting the broad
band spectrum and lightcurves of the source we identify several microlensing
caustic crossing events, and study the details of variability of the source
during these events. The caustic crossings of image A on MJD 55150 and 55500
produce strong variations of the overall X-ray flux from the source. In the
soft X-ray band, the caustic crossing events are characterised by the
exponential growth / decay of the flux ratio between the source images with the
exponentiating time scale T_d~60 d, which corresponds to the caustic transit
time of the source of the size ~10^{14} cm. Variability induced by the
microlensing dominates the overall variability of the sum of the fluxes of four
images of the source which should also be detectable in the hard X-ray
lightcurve, if the hard X-ray source is comparably compact. Non-detection of
the caustic crossing events in the SWIFT/BAT lightcurve of the source indicates
that geometry of the region of emission of X-rays with energies above 15 keV is
different from that of the lower energy X-rays, with the hard X-ray emission an
order of magnitude larger in size.
