The warmth we feel from a fire comes from energy as it radiates outwards in the form of heat. The hot gas products rise because they are less dense than the surrounding, cooler air. The gases carry with them soot particles that glow yellow-orange because of their high temperature.
In a bushfire or campfire, it is the glowing soot that we experience as flames. Flames actually extend well above where we can see them. As the soot moves higher up, it cools and emits light in colours that we cannot see, such as infrared light.
The short answer for the literal question is hot smoke. I always hated the dodge of saying ‘fire is a process.’ The state of matter of a visible flame is a solid. It’s just atomized, and all the organic compounds are energetically trying to turn back into gas.
Rain is only rain when it’s in midair, but you’d be a fool to insist that means it’s not liquid. It’s fucking water.