The reuse of food industry by-products constitutes one of the essential pillars of the change from a linear to a circular economic model. Drying is one of the most affordable techniques with which to stabilize by-products, making their subsequent processing possible. However, it can affect material properties. The objective of this study was to assess the effect of the drying temperature on the drying kinetics and final quality of the main artichoke processing by-products, bracts and stems, which have never been studied as independent materials. For this purpose, air drying experiments at different temperatures (40, 60, 80, 100 and 120 °C) were carried out. The alcohol insoluble residue (AIR) and the total phenolic content (TPC), antioxidant capacity (AC) and vitamin C (VC) of the fresh and dried samples were determined. The bracts dried faster than the stems, increasing drying rate with temperature. The two by-products presented relatively large amounts of AIR, the content being higher in bracts, but better functional properties in stems. The TPC, AC and VC values of the dried samples decreased in relation to the fresh samples, with the temperatures of 40 °C (bracts) and 120 °C (stems) being the most adequate for the purposes of preserving these characteristics.