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It depends on the nature of the supergiant and the white dwarf. A new white dwarf might have a temperature of 100,000 kelvin so much hotter than any supergiant, but important to in that it is constantly cooling because the star is dead and there is no fusion. A blue supergiant is a new star with a fusion temperature of around 20,000 kelvin. A red supergiant might be cooler than this, maybe 4,000 kelvin. As long as stable fusion is happening these temperatures remain pretty constant. If you remember that a white dwarf is a dead star then comparing surface temperatures will depend on how long it has been cooling. Eventually it will be the same temperature as the universe itself so really cold. So it will either be hotter, cooler or the same temperature! 😆
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What do all ions have in common in terms of their electronic structure?