A rapid increase in the electrical power on board vehicles has presented significant challenges to their thermal management. One proposed solution for large vehicles is the use of thermal energy storage (TES) modules containing phase change material (PCM) to quickly absorb large thermal loads, buffering fast thermal transients to reduce peak cooling requirements. However, the inherent nonlinearity and multi-timescale nature of vehicles with phase change energy storage must be addressed in control design. This paper presents a hierarchical hybrid model predictive control (MPC) framework to meet this need. A hierarchical control framework coordinates between the relatively slow phase change dynamics of the TES and relatively fast temperature dynamics elsewhere, excited by highly transient loading. Switched linear models are used to approximate nonlinearities across a wide range of operating conditions, resulting in hybrid MPC formulations that balance model accuracy and computational burden. The proposed approach is demonstrated in simulation on a candidate thermal management system with multiple TES modules.