The performance of a radiatively cooled instrument is investigated in the context of optomechanical quantum experiments, where the environment of a macroscopic particle in a quantum-superposition has to be cooled to less than 20\,K in deep space. A heat-transfer analysis between the components of the instrument as well as a transfer-function analysis on thermal oscillations induced by the spacecraft interior and by dissipative sources is performed. The thermal behaviour of the instrument in an

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... rbit around a Lagrangian point and in a highly elliptical Earth orbit is discussed. Finally, we investigate further possible design improvements aiming at lower temperatures of the environment of the macroscopic particle. These include a mirror-based design of the imaging system on the optical bench and the extension of the heat shields.