Acrocomia aculeata is a palm tree typical of the Brazilian savanna. Oils extracted from the pulp and kernel of Acrocomia aculeata fruits have gained considerable attention mainly due to their nutritional and medicinal features. Despite their potential applications, a detailed analysis of their oxidative stability is still needed. The present study shows a close analysis of the oxidative stability of the oils obtained from the kernel and pulp of Acrocomia aculeata fruits, evaluating the influence of the intrinsic antioxidants and the fatty acid composition on the oil’s thermal stability. A complete characterization of the physical-chemical and optical properties of the oils was performed. The results showed that 66% of the fatty acids present in the pulp oil are unsaturated, while 75% are saturated in the kernel oil. A higher content of intrinsic antioxidants was obtained in the pulp oil, and an induction period (at 110 °C) of 65 and 43 h was determined for the pulp and kernel oil, respectively. Additionally, oil absorption increases due to the formation of degradation products, and a new fluorescent compound was formed during the oil oxidation process at 110 °C. Even though the pulp presented a high content of unsaturated fatty acids, the pulp oil was more stable than the kernel oil due to its higher content of intrinsic antioxidant, especially carotenoids. The results also demonstrated that oil oxidation can be optically determined by analyzing the absorption at 232 and 270 nm, as well as the emission at 424 nm.