The PHENIX collaboration presents first measurements of low-momentum (0.4<pT<3 GeV/c) direct-photon yields from Au+Au collisions at sNN=39 and 62.4 GeV. For both beam energies the direct-photon yields are substantially enhanced with respect to expectations from prompt processes, similar to the yields observed in Au+Au collisions at sNN=200. Analyzing the photon yield as a function of the experimental observable dNch/dη reveals that the low-momentum (>1 GeV/c) direct-photon yield dNγdir/dη is a smooth function of dNch/dη and can be well described as proportional to (dNch/dη)α with α≈1.25. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different A+A collision systems. At a given beam energy, the scaling also holds for high pT (>5 GeV/c), but when results from different collision energies are compared, an additional sNN-dependent multiplicative factor is needed to describe the integrated-direct-photon yield.