The capacitor is one of the key components in modular multilevel converter (MMC) systems. Its thermal characteristics have a significant impact on its lifetime and the reliability of the submodule. Various circulating current control strategies have been proposed to eliminate the second-harmonic circulating current or minimize the capacitor voltage ripple. However, the influences of these control methods on the capacitor thermal stress remain an unsolved problem. This article introduces a comprehensive loss and thermal model considering capacitor clusters inside the arm of the MMC. The thermal stress and distribution are analytically solved based on the mission profile of the MMC and capacitor parameters. Then, a circulating current control method for optimal thermal stress of capacitors is revealed by utilizing the proposed thermal model. Finally, simulation and experimental results based on a mission profile emulator for MMC capacitors are developed to verify the proposed method.