Imagine an earthlike planet in the habitable zone of Alpha Centauri B. Call it ACBc (although I am not sure ACBb has been confirmed). When ACA and ACB are closest to one another, they are about 11 AU apart (similar to the distance from Saturn to the sun). Rounding to 10 AU, this means that the irradiance from ACA on our hypothetical ACBc is about 1% of what it would be if ACA and ACBc were one AU apart, like the sun and the earth. Since ACA has 1.5 times the sun's luminosity, that would work out to about 1.5% of the sun's apparent brightness from the earth.
But, when ACA and ACB are farthest apart (which is a larger part of the time because they are moving more slowly then), the distance is more than 3.5 times as great, so the apparent brightness is more than ten times smaller.
This means that, for maybe ten consecutive earth-years out of every 79, ACBc would be getting an extra 1-1.5% irradiance, averaged over the surface of the planet. By comparison, the sun's apparent brightness is about 3.4% greater when the earth at perihelion than at aphelion. This does warm the earth slightly near perihelion, but the effect is swamped at most locations by the tilt of the earth's axis. Perihelion is during the northern winter, when it is coldest for many of the planet's inhabitants.
Still, the effect is not zero, and it would accumulate over several years. Has anyone done any modeling for how that would affect the climate for that period of time when ACA and ACB are near minimum distance? Is there a rule of thumb for solar forcing to suggest how much the average temperature would increase per year over those years?