Recombination processes in GaP/GaNP core/shell nanowires (NWs) grown on Si are studied by employing temperature-dependent continuous wave and time-resolved photoluminescence (PL) spectroscopies. The NWs exhibit bright PL emissions due to radiative carrier recombination in the GaNP shell. Though the radiative efficiency of the NWs is found to decrease with increasing temperature, the PL emission remains intense even at room temperature. Two thermal quenching processes of the PL emission are found to be responsible for the degradation of the PL intensity at elevated temperatures: (a) thermal activation of the localized excitons from the N-related localized states and (b) activation of a competing non-radiative recombination (NRR) process. The activation energy of the latter process is determined as being around 180 meV. NRR is also found to cause a significant decrease of carrier lifetime.