Does fire have a shadow?

Does fire have a shadow? Flames look like light, so most people say no. But in bright sunlight, a fire can cast a faint shadow. The hot air above a flame bends light passing through it, and soot particles in the flame block some light too. Next to a bright lamp in a dark room, though, you won't see much. So what's your answer: yes, no, or it depends?

Breakdown and comments appear here once you answer.