Per- and polyfluoroalkyl substances (PFAS), which are considered an international problem due to their persistence in the environment, need to be properly treated in the end. In the destruction method by incineration, basic data are required to quantify the destruction characteristics of the target substance and the temperature-dependent behavior of its by-products. In this study, we conducted incineration tests targeting perfluorooctanoic acid (PFOA) and perfluorooctadecanoic acid (PFOcDA). The tests were conducted at temperatures ranging from 450 °C to 1000 °C in a pure air atmosphere, with a residence time of 2 s. The incineration tests at 850 °C achieved a destruction efficiency (DE) of 99.999% for both PFOA and PFOcDA. The DE significantly decreased at temperatures below 700 °C. Various by-products were identified during these tests, including short- and long-chain carbon compounds with ether bonds. Byproducts such as PFOA and polyfluoroalkyl ether carboxylic acids (PFECAs) were produced during the low-temperature incineration of PFOcDA. The amount of by-products produced increased as the temperature decreased, but short-chain by-products increased at incineration temperatures from 450 to 700 °C. The capture media for the by-products varied depending on the carbon chain length of the PFCAs. The proportion captured by glass filters, adsorbents, and sodium hydroxide increased sequentially from long-to short-chain compounds. An examination of the distribution patterns of PFCAs across the different media revealed their predominant presence in the exhaust gas. Sufficient incineration at temperatures above 850 °C is considered necessary for effective destruction of PFOA and PFOcDA, including their by-products.