In this paper, the focus is on ice clamping of workpieces using feedback-controlled Peltier cells, which represents a novel nonlinear control application. As only the hot-side temperature is accessible for measurements, an Unscented Kalman filter (UKF) estimates the temperatures on both the hot and cold sides of the Peltier element and a lumped disturbance heat flow acting on the cold side. These estimates are employed in linearized discrete-time model predictive control (MPC), which is adapted in each time step based on Taylor linearizations around desired trajectories, also considering the predicted future linearization errors, and tracks a given cold-side temperature profile despite interfering heat inflow from the machining process. Here, the nonlinear system model is exploited to calculate favorable desired values that correspond to low currents, minimizing the overall energy consumption and avoiding another possible operating point with high currents. The achieved tracking precision and estimation accuracy is pointed out in simulation results for a typical ice clamping scenario subject to disturbances.