The temperature control of an insulated cool box (ICB) can be efficiently provided by model predictive control. However, if the cooling capacity is supplied by redundant refrigeration circuits (RCs) with both continuous and switched control variables, the overall control design becomes complex: (1) Time constants of the ICB and RCs differ by a factor of approximately 100. (2) Switched and continuous control variables require mixed-integer optimisation. (3) Power consumption, wear, control performance and output tracking call for multi-objective optimisation. In this work a global linear Model Predictive Controller (MPC) is designed to compute a desired cooling capacity at a low sampling rate over a long prediction horizon, while a mixed-integer optimisation (MIO) provides the actual, optimally modulated cooling capacity utilising a fast sampling rate and a short prediction horizon. The control concept is presented, the interaction between the two MPC instances is described, stability and feasibility are discussed, and simulation results demonstrate the performance of the concept. (C) 2019 Elsevier Ltd. All rights reserved.