A self-consistent finite temperature relativistic quasiparticle random phase approximation (FT-RQRPA) based on relativistic energy density functional is developed to describe temperature effects in electromagnetic transitions. The isotopic chain of $^{100-140}$Sn nuclei is considered to study the evolution of electric dipole (E1) and magnetic dipole (M1) transitions at temperatures ranging from $T=$ 0 to 2 MeV. The analysis reveals that E1 giant resonance is moderately modified with temperature increase, and new low-energy excitations appear at higher temperatures, making a pronounced impact, particularly in neutron-rich nuclei. This happens because of the unblocking of new transitions above the Fermi level due to thermal effects on single-particle states. However, the M1 strength peaks undergo a notable shift towards lower energies in Sn nuclei, primarily attributed to the decrease of spin-orbit splitting energies and the weakening of the residual interaction. This effect is particularly pronounced, especially above critical temperatures ($T_c$), where the pairing correlations vanish. In conclusion, the E1 and M1 responses demonstrate considerable dependence on temperature, and their effects could be important in modeling gamma strength functions and their applications in astrophysically relevant nuclear reaction studies.