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This paper investigates the impact of cold-start conditions on the fuel-saving potential and the associated optimal energy controller of a mechanical hybrid powertrain. The mechanical hybrid powertrain uses a flywheel system to add fuel-saving functionalities to a conventional powertrain, which consists of an internal combustion engine and a continuously variable transmission (CVT). The cold-start conditions refer to a low powertrain temperature, which increases the frictional power dissipation in the engine and transmission, and a stationary (or energyless) flywheel system, which must be energized to a minimum energy level before it can be effectively utilized. The heating of the powertrain and the initialization of the flywheel system can be influenced by the energy controller, which controls the power distribution between the engine, the flywheel, and the vehicle. The energy controller aims at minimizing the overall fuel consumption for a given driving cycle. The optimal energy controller is found analytically for a simplified model to gain qualitative insights in the controller and numerically using dynamic programming for a detailed model to quantify the impact on the fuel consumption. The results show that the cold-start conditions have a significant impact on the fuel-saving potential, yet a negligible impact on the optimal energy controller. The latter result implies that the temperature state can be eliminated from the state space of the energy controller, which is an important step toward the design of an effective yet simple energy controller suitable for real-time implementation.