The gamma -ray strength function (gamma SF) is essential for understanding the electromagnetic response in atomic nuclei and modeling astrophysical neutron capture rates. We introduced a microscopic description of both electric dipole (E1) and magnetic dipole (M1) gamma SFs that includes finite-temperature effects within relativistic density functional theory. The temperature dependence of the total electromagnetic gamma SFs shows significant modification in the low-energy region due to thermal unblocking effects, essential for agreement with recent particle-gamma coincidence data from the Oslo method. An investigation of the electric and magnetic contributions to the total gamma SF in hot nuclei indicates that the M1 mode becomes more prominent in the low-energy region, different than what is known at zero temperature. This microscopic approach offers new insights into the interplay between E1 and M1 gamma SFs at finite temperature and opens new perspectives for future studies of (n, gamma ) reactions and nucleosynthesis in hot stellar environments.