I'd imagine it's (total amount of sunlight hitting the visible portion of that roof) * (… the solid angle the window occupies, relative to the roof?) The first

I'd imagine it's (total amount of sunlight hitting the visible portion of that roof) * (… the solid angle the window occupies, relative to the roof?) The first portion of that equation is hot: roofs have a lot of sq. ft.'age, and a fair bit of sunlight strikes them. But the second part is well the other direction: the window probably doesn't occupy a whole lot of the field of view of the roof: i.e., mostly, any ray emitted randomly from any point on the roof is likely going to be skyward, so assuming it emits the heat/light out equally in all directions, your window only gets a small fraction. The portion coming in your window doesn't go back out to space but I don't think that's a big deal?