Textile wastewater containing dyes poses significant environmental hazards. Advanced oxidative processes, especially the heterogeneous photo-Fenton process, are effective in degrading a wide range of contaminants due to high conversion rates and ease of catalyst recovery. This study evaluates the heterogeneous photodegradation of the azo dyes Acid Red 18 (AR18), Acid Red 66 (AR66), and Orange 2 (OR2) using magnetite as a catalyst. The magnetic catalyst was synthesized via a hydrothermal process at 150 °C. Experiments were conducted at room temperature, investigating the effect of catalyst dosage, pH, and initial concentrations of H2O2 and AR18 dye. Kinetic and thermodynamic studies were performed at 25, 40, and 60 °C for the three azo dyes (AR18, AR66, and OR2) and the effect of the dye structures on the degradation efficiency was investigated. At 25 °C for 0.33 mmolL−1 of dye at pH 3.0, using 1.4 gL−1 of the catalyst and 60 mgL−1 of H2O2 under UV radiation of 16.7 mWcm−2, the catalyst showed 62.3% degradation for AR18, 79.6% for AR66, and 83.8% for OR2 in 180 min of reaction. The oxidation of azo dyes under these conditions is spontaneous and endothermic. The pseudo-first-order kinetic constants indicated a strong temperature dependence with an order of reactivity of the type OR2 > AR66 > AR18, which is associated with the molecular size, steric hindrance, aromatic conjugation, electrostatic repulsion, and nature of the acid–base interactions on the catalytic surface.