The InGaAs/AlGaAs quantum wells have been extensively applied to quantum well infrared photodetector of mid-wavelength. In this letter, four samples of 2.4 nm In0.35Ga0.65As/40 nm Al0.34Ga0.66As multi-quantum wells are grown by molecular beam epitaxy with the InGaAs wells growing all at a temperature of 465℃ but the AlGaAs wells growing at temperatures of 465℃, 500℃, 545℃, and 580℃ respectively. The dependence of InGaAs quantum well strain relaxation on the AlGaAs growth temperature is systematically studied by photoluminescence spectroscopy and X-ray diffraction and then the thermal-induced relaxations of three key-stages are clearly observed in the following temperature ranges. 1) 465-500℃ for the stage of elastic relaxation: the phase separation begins to take place with a low defect density; 2) 500-545℃ for the transition stage from elastic relaxation to plastic relaxation: the phase separation will be further intensified with defect density increasing; 3) 545-580℃ for the fast stage dominated by elastic relaxation and the defect density will sharply increase. Especially when AlGaAs temperature increases to 580℃, a very serious plastic relaxation will take place and the InGaAs quantum well will be dramatically destroyed.