The substrate temperature (Ts) dependence (350–700 °C) of GaAs and Ga1−y InyAs growth rates was investigated in metalorganic molecular beam epitaxy (MOMBE), using triethylgallium (TEG), trimethylindium (TMI), and solid arsenic (As4) sources. For GaAs growth, four distinct Ts dependent regions are observed, including a weak desorption process (500–650 °C) characteristic of MOMBE, preceding atomic Ga desorption (Ts >650 °C). When adding a TMI flux to grow Ga1−yInyAs, this desorption process was much enhanced up to 550 °C, and then decreased above 550 °C when the In desorption phenomenon takes place. Correlatively, the In alloy composition peaks at 550 °C. The same dependence was observed in Ga1−yInyAs growth using solid In and TEG sources. However, in Ga1−xAlxAs growth using solid Al or triethylaluminum (TEA) and TEG sources, the weak desorption observed in GaAs MOMBE was strongly minimized. From these results, possible growth mechanisms are discussed.