Why were there global firestorms after the K-Pg asteroid impact?

I read that the asteroid smacked into earth, blew up with the force of billions of nuclear bombs, and ejected billions of kg of limestone rock into the air. That much makes sense to me. But papers like these say that all the rocks raining back down heated the atmosphere to the point where it broiled many of the dinosaurs alive and ignited forest fires pretty much everywhere. Why would tiny rocks raining down heat the air so much?