In this article, the design of an observer realized as an extended Kalman filter (EKF) is presented for a nonlinear thermoelectric system, characterized by a Peltier cell (PC). The task of the observer is to estimate the temperatures of the cold and warm side of the PCs, e.g., for control purposes. In particular, the cold-side temperature is to be monitored in the cooling system that is used to clamp workpieces by freezing of water in a novel industrial manufacturing process. The estimation of these temperatures is done during the milling phase in which a mill generates an abrupt change in the temperature to be controlled. Through the developed EKF, a sensorless control can be realized in order to control the cold-side temperature without the use of a sensor. Sensorless control has the advantages of minimizing costs, installation efforts, maintenance, measurement noise, and saving space in installation. Even during the milling phase, the EKF shows excellent estimation results that are obtained from real measurements obtained from a dedicated test bench.