In this paper, the design of a reduced order observer is presented for a nonlinear thermoelectric system, characterized by a Peltier cell (PC). The task of the observer is to estimate the temperature of the PC's cold side in a cooling system that is used to clamp workpieces by freezing of water in a novel manufacturing process. Due to strongly nonlinear thermoelectric interactions inside the system, an additional Extended Kalman Filter (EKF) is proposed to identify important system parameter. The reduced observer design shows a simple but accurate way to determine the cold-side temperature for further computations as well as for additional controller design approaches.