Chernobyl was a Light Water Reactor...it used water as coolant and moderator. The fire was the result of the lack of coolant...the fuel got so hot because there was no water to remove the heat...it burned.
My father is a nuclear engineer, and I read the report about the accident that he possessed.
There is a famous photo of Chernobyl where flames are seen in the heart of the reactor. That is graphite coolant burning.