<p>This paper presents a new adaptive periodic non-collocated output tracking control approach for a parabolic PDE-ODE cascaded system with parametric uncertainties. The proposed control framework is developed to guarantee high-precision output tracking performance for periodic reference inputs. First, the periodic non-collocated output tracking problem is transformed into a collocated one by solving a boundary value problem associated with the signal model of the reference input. Subsequently, based on the periodic characteristics of the desired trajectory, an enhanced PDE-ODE reference system is constructed by introducing an approximate internal model of periodic signals. Then, an adaptive parameter update law is devised to accurately estimate the unknown parameters using the Kreisselmeier’s dynamics regressor extension and mixing strategy. Furthermore, by combining the repetitive controller with the estimated parameters, an adaptive periodic output tracking control law is developed to ensure that the system output precisely follows the desired trajectory. The stability conditions of the closed-loop system, convergence analysis of the error signals, and detailed design procedures for both the controller and the adaptive parameter estimator are provided. Finally, the proposed method is applied to a temperature regulation system of a heating metal rod. Simulation results are presented to validate the effectiveness and robustness of the proposed adaptive repetitive control scheme, and comparative studies are conducted to demonstrate its superior performance.</p>