In modern high-performance aircraft, the Fuel Thermal Management System (FTMS) plays a critical role in the overall thermal energy management of the aircraft. Actuator and state constraints in the FTMS limit the thermal endurance and capabilities of the aircraft. Thus, an effective control strategy must plan and execute optimized transient fuel mass and temperature trajectories subject to these constraints over the entire course of operation. For the control of linear systems, hierarchical Model Predictive Control (MPC) has shown to be an effective approach to coordinating both short- and long-term system operation with reduced computational complexity. However, for controlling nonlinear systems, common approaches to system linearization may no longer be effective due to the long prediction horizons of upper-level controllers. This paper explores the limitations of using linear models for hierarchical MPC of the nonlinear FTMS found in aircraft. Numerical simulation results show that linearized models work well for lower-level controllers with short prediction horizons but lead to significant reductions in aircraft thermal endurance when used for upper-level controllers with long prediction horizons. Therefore, a mixed-linearity hierarchical MPC formulation is presented with a nonlinear upper-level controller and a linear lower-level controller to achieve both high performance and high computational efficiency.