It hasn't been proven at all, in fact, a lot of astrobiologist think that the most likely places to find life off of Earth is on some of the moons that have liquid water oceans beneath a frozen exterior. Water can be liquid because of the heat generated by tidal friction.
I think if your smaller sun / larger sun model is like mercury and our sun, then days and night could be like what we experience here, since your planet will have once side facing both of them all of the time.
Also, having a planet 1/3 the size of earth might be a problem with radiation. If...