Photoluminescence (PL) spectra of GaInNAs/GaAs multiple quantum wells grown on a GaAs substrate by molecular beam epitaxy are measured in a range of temperatures and excitation power densities. The energy position of the dominant PL peak shows an anomalous S-shape temperature dependence instead of the Varshni relation. By careful inspection, especially for the PL under lower excitation power density, two near bandedge peaks are well identified. These are assigned to carriers localized in nitrogen-induced bound states and interband excitonic recombinations, respectively. It is suggested that the temperature-induced switch of such two luminescence peaks in relative intensity causes a significant mechanism responsible for the S-shape shift observed in GaInNAs. A quantitative model based on the thermal depopulation of carriers is used to explain the temperature dependence of the PL peak related to N-induced bound states.