Quaternary alloys InGaGdN with In content of 23% and 14% (Gd % 1% in both) are successfully grown with a sufficient quality to investigate the temperature behavior of photoluminescence (PL). A temperature-independent peak position is found for the sample with In content of 23%, while the sample with In content of 14% shows a weak temperature dependence.A theoretical model to explain the temperature dependence of the band gap of semiconductors is developed, where the interband mixing and the inner stress caused by the difference of the thermal expansion among the component alloys are taken into account.