The measurement of direct photons from Au$+$Au collisions at $\sqrt{s_{NN}} = 39$ and $62.4$ GeV in the transverse momentum range $0.4 < p_T < 3$ GeV/$c$ is presented by the PHENIX collaboration. A significant direct photon yield is observed in both the systems. A universal scaling is observed when the direct photon $p_T$ spectra for the different center of mass energies and for different centrality selection at $\sqrt{s_{NN}} = 62.4$ GeV is scaled with $(dN_{ch}/d\eta)^{\alpha}$ with $\alpha=1.21 \pm 0.04$. This scaling also holds true for direct photon spectra from Au$+$Au collisions at $\sqrt{s_{NN}} = 200$ GeV measured by PHENIX, as well as the spectra from Pb$+$Pb at $\sqrt{s_{NN}} = 2760$ GeV published by ALICE. It is also demonstrated that the scaling power $\alpha$ seem to be independent of $p_T$, center of mass energy, and collision centrality. The spectra from different collision energies, have a similar shape up to $p_T$ of $2$ GeV/$c$. They are concave with an increasing local inverse slope $T_{eff}$ that is $0.174\pm0.018$ GeV/$c$ in the range $0.4<p_T<1.3$ GeV/$c$ and increases to $0.289\pm0.024$ GeV/$c$ for $0.9<p_T<2.1$ GeV/$c$. The observed similarity of low $p_T$ direct photon production from $\sqrt{s_{NN}} = 39$ GeV to $2760$ GeV suggests a common source of direct photons for the different collision energies and event centrality selections, and that the possible differences in the space time evolution do not alter direct photon emission significantly.