Lord Macaulay, in his epic poem, Virginia, favours "under."

"Here, in this very Forum, under the noonday sun,
In the sight of all the people, the bloody deed was done."

But Noel Coward - also a superb crafter of the English language - favours, "in."

"Mad dogs and Englishmen
Go out in the noonday sun."

That your pick, as the site foreman said to the confused Irishman, as he offered him the choice of two shovels.
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I'm immortal until proven otherwise