This is basically a world-building question, but I'm looking for a scientifically based answer, so I'm posting here.
Imagine a fairly earth-like planet- Lets call it Planet X. Planet X has an earth-like compisition, size, gravity, and such.
Planet X is also tidally locked to its sun, Sun 1. It's an eyeball planet, a scorching desert on one side, freezing cold on the other, with a narrow habitable band inbetween.
However, this is a binary star system. There are two suns- Sun 1 and Sun 2. Planet X orbits Sun 1, with Sun 2 orbiting at a distance. (or, possibly, Sun 1 orbits Sun 2.)
My question is this: Is there any way for this to happen, that Sun 2 is close enough to melt (some) of the ice on the backside of Planet X when it faces Sun 2? That this could cause a weather cycle on Planet X, when the floods come from the locked away ice melting?