How much does my secondary star heat the planet orbiting my primary star?
In this question I asked about the lighting patterns from this system:
A really helpful answer there explained when the planet is getting how much illumination.
This question is about heat. On earth I have a pretty good sense of the temperature variations over the course of the year at different latitudes. I'm not sure how to work that out when there are two stars in play, one more distant but, hey, it's still a star and stars radiate heat. I want to make sure that most of my planet is inhabitable throughout the year, like Earth; it's ok if some regions (poles) are too hot (or too cold) during certain seasons. Note that at some times of the year the second star is not visible from the planet, though presumably some of its heat still gets there. At the point marked "max double-day", all points on the planet are getting continuous heat (no night).
Is heat simply a proportion of initial amount and distance, or is it more complicated? How important is the "time off" (night) in regulating temperature?
The size and class of the secondary star seem relevant. I want the secondary star to cast enough light to matter on the planet, like to the level of a dreary rainy day (not just moonlight levels of light). An answer there suggests that I could put the secondary star in a reflection nebula. Beyond that, the size and class of the secondary star are not yet determined -- I'm happy to work with anything that gives me the light I want without frying my planet.