Climate on a world with a Sun of varying luminosity

Given the daylight cycle discussed here (see the graph in the selected answer), suppose that the moon revolves in the equatorial plane, at a distance sufficient to light (barely) the poles, avoiding a snowball scenario. Suppose also that the maximum illumination at one instant (at the maximum of the cycle and at the equator) is equal (or slightly less than) that of Earth's sun. I imagine this planet as divided in two large land masses (supercontinents) divided by a huge sea.

What could be the consequences on the planet's climate? How much big would be the temperature excursion between the maximum daylight and the minimum daylight? How much strong would be winds between the twilight regions and the equator?

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Climate on a world with a Sun of varying luminosity

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