Dragon's Flame, Magical?

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Originally Posted by The Might

Now to the dragon idea, the basic theory in pretty much all newer dragon works is that the fire is only created in their mouths through the mixture of two separate chemical substances. And this makes quite a lot sense. Anything that can be pierced by a sword isn't probably capable of taking that much heat. Thus, a dragon himself wouldn't really need to take that heat himself.

Well, from Tolkiens description of dragons it's clear that their bodies were strong heat sources even while not breating fire. Smaug indeed seemed to glow steadily, like burning charcoal, bringing heat as well as light to his hall. Also, when Glaurung enters the river outside Nargothrond, the water boils, and vast steams and blinding vapours cover the area. If a dragons cools down, it seems to be unable to breath fire and is less potent, more resembling a great, slimy lizard.

In that movie with dragons in it "Reign of Fire", the fire was caused by a mix of chemicals as you described. I don't think Tolkien imagined his dragons to be anything like those creatures.