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This paper describes the thermal design and analysis of the Electronic Unit (EU) of a Microgravity Vibration Isolation System (MVIS) that will ensure the active isolation of the European Space Agency's Fluid Science Laboratory (FSL) payload from vibration induced by the International Space Station (ISS) structure. The FSL is equipped with optical and electronic devices that are very sensitive to vibration, thermal distortion, temperature change and ElectroMagnetic Interference (EMI). The MVIS has to provide a vibration attenuation of -40dB within the range of 0.1-100Hz without inducing thermal or electromagnetic interferences. The sensitive FSL instruments are mounted in a floating structure called the Facility Core Element (FCE), whereas the rest of the FSL electronics, mechanics and cooling systems are fixed to the International Standard Payload Rack (ISPR).