Intensity interferometry of thermal photons, having transverse momenta kT ≈ 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 kT 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.