It occurred to me that part of the problem is answered by a circumbinary planet. In this configuration, the planet warms up as it approaches the two binary stars, but cools off when one star passes in front of the other.

Unfortunately, that doesn't explain the increase in temperature during winter. I could throw in a third star, maybe a red dwarf, that was also in a circumbinary orbit. Our intrepid planet would approach it just as it happens to be closer in its own orbit.

For this sort of arrangement to occur, there would have to be some kind of orbital resonance going on. Does anyone have the math and the desire to try that out?

It occurred to me that part of the problem is answered by a circumbinary planet. In this configuration, the planet warms up as it approaches the two binary stars, but cools off when one star passes in front of the other.

Unfortunately, that doesn't explain the increase in temperature during winter. I could throw in a third star, maybe a red dwarf, that was also in a circumbinary orbit. Our intrepid planet would approach it just as it happens to be closer in its own orbit.

For this sort of arrangement to occur, there would have to be some kind of orbital resonance going on. Does anyone have the math and the desire to try that out?

Another possibility is that one of the binary stars (a white dwarf stealing mass from the other star) erupts in a supernova while the planet is furthest from the pair. This is a condition that might last just long enough for life and intelligence to arise on the planet and realize that the white dwarf is about to go kerblooey for good.