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An investigation was made of the cooling of power transistors in a space environment, where the only available mode of heat transfer is that of conduction to a heat sink and radiation from the heat sink to space. An attempt was made to minimize the thermal resistance between transistor case and heat sink, allowing the transistor to dissipate as much power as possible while maintaining its temperature within the maximum tolerable level to prevent thermal runaway. Further, it was necessary to electrically insulate the transistor from the heat sink. The use of beryllium oxide washers provided electrical insulation, while adding very little to the thermal resistance between case and sink, the BeO being a good heat conductor. However, the problem of contact thermal resistance at each interface arose, especially in vacuum this contact resistance providing practically al the thermal resistance between case and sink. The effect on the contact resistance of surface pressure, insertion of foils, and soldering was examined. It was concluded that, for most efficient heat sinking, indium foil should be inserted at each interface, the indium foil having the effect of reducing the contact resistance in vacuum by a factor of 8.