We investigated theoretically the temperature dependence of the quantum optical tran- sition of quasi-2-dimensional Landau splitting, in GaN and GaAs. We apply the quantum transport theory (QTR) to a system of electrons confined in a potential. We use the projected Liouville equa- tion method with equilibrium average projection scheme (EAPS). Through the analysis of this work, we found increasing optical quantum transition line shapes (QTLSs) and the quantum tran- sition line widths (QTLWs) in GaN and GaAs with increasing temperature. We also found the temperature dependences of the scattering factor functions: (T) of GaN < (T) of GaAs in the temperature region 50 K < T and (T) of GaAs < (T) of GaN in the temperature T < 50 K and = 394 µm.