I recently read that temperatures on the moon can vary from -100 °C in the shade to 100 °C in the sunny part.
How did astronaut suits cope with these extreme temperatures? Is the same technology used in other fields today?
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So, the surface temperature can even vary a bit more:
|Equator||100 K||250 K||390 K|
|85°N||N/A||150 K||230 K|
But that problem is not as big as it looks. The Moon can be considered to be surrounded by vacuum . This means:
Space suits or space ships/capsules are (nearly) always white (maybe not always "clean white") or metallic (silver, golden). This colour is chosen, so minimum thermal energy is absorbed, but also minimum is radiated.
So, there is a situation, where heated objects can keep thermal energy quite well. Additionally, Apollo missions only landed on the sunny part of the moon. There was no Apollo landing in a "lunar night". So the surface temperatures had been quite stable.
This all is reducing the problem to situations, where an astronaut grabs for something or stands on the moon surface. In this case, there is physical contact between the hot surface and the space suit.
So building a lunar space suit it is important to use materials capable of handing these temperatures and isolating it enough so the person inside does not get hurt, by using materials such as: Nylon, Kapton or Teflon.
Besides the suits and space craft had thermal regulation ("AC") to cope with thermal energy from inside, but that would be another question.
Is the same technology used in other fields today?
Yes, I call it oven gloves and use it while getting my pizza ;-)