Might be a faulty fan - computer gets too hot and shuts itself off. Happened to an old laptop I had.
This was my first thought too. Is there a lot of dust and crap in the fan? Give it a bit of a hoover (gently).
@mattty started
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This was my first thought too. Is there a lot of dust and crap in the fan? Give it a bit of a hoover (gently).