The math for the second star should be right. And it pretty much should just be a constant 9 K increase for the whole planet. Doing some sketches, sometimes the second star would cause seasons to be more mild, sometimes more extreme. It would go on a very slow cycle though. Hundreds of years if not longer for it to change from extreme to mild (per hemisphere). Given how minor the change is, it's probably best to just ignore it except for "cool second star in the sky" kind of stuff.