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What is the highest recorded temperature in space? I'm not asking about Planck temperature that is a fraction of a second before the Big Bang. I'm asking about the temperature that has been recorded by an instrument.

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Well this infograhic puts gas heated by a supernova at about 55 million Celsius.

And that's not even the highest temperature we can just "find" out there, even if we discard supernovae and stellar cores. The gas in a cluster of galaxies (the ICM) can have temperatures on the orders of 10 million to 100 million Kelvin. Such a high temperature gas emits high energy photons such as X-rays via bremsstrahlung radiation, and these are observable (and have been observed) by X-ray telescopes.

There's this review article from 2003 that covers the basic methodologies and measurements made on ICMs, including (but decidedly not limited to) temperature.

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