  Intensity interferometry of thermal photons, having transverse momenta $k_T
\approx $ 0.1 -- 2.0 GeV, produced in relativistic collision of heavy nuclei is
studied. It is seen to provide an accurate information about the temporal and
spatial structure of the interacting system. The source dimensions and their
$k_T$ dependence revealed by the photon interferometry, display a richness not
seen in pion interferometry. We attribute this to difference in the source
functions, the fact that photons come out from every stage of the collision and
from every point in the system, and the fact that the rate of production of
photons is different for the quark-gluon plasma, which dominates the early hot
stage, and the hadronic matter which populates the last phase of the collision
dynamics. The usefulness of this procedure is demonstrated by an application to
collision of lead nuclei at the CERN SPS. Prediction for the transverse
momentum dependence of the sizes for SPS, RHIC, and LHC energies are given.
