Gliese 581 g

The planet is probably tidally locked to its red dwarf sun, with one side in perpetual day, where the red dwarf sun would simply remain in the same spot in the sky indefinitely. while the other side of the planet would remain in perpetual night. However if Gliese 581g has a substantial atmosphere, the winds and weather patterns should easily prevent the day side from becoming too hot and prevent the atmosphere from freezing on the night side.