The heat can and does suck the oxygen out of them as fuel. In the Dresden firestorm, thousands suffocated in basements and shelters.
Yes. Dresden was an extraordinary massive firestorm, as one can only get with vast amounts of fuel, and overwhelming deployment of incendiary devices.
We know the shelters were oxygen starved because the bodies inside burst into flames when rescuers cracked open the doors and let air in.
Slaughterhouse-Five, a novel by Kurt Vonnegut is based on his World War II experiences as a POW held in a slaughter house basement refrigerator in Dresden. He related that when they left their shelter they saw perfectly normal "people sitting on benches near the sidewalk, as if they were waiting for the trolly. All were dead from suffocation."
Vonnegut was never quite the same...
Regards,
GtG