It's both actually, birch AND willow -- I guess it depends on where you live, which is more common -- down here in the south, there ain't a lot of birch trees (like, none, unless some enterprising yankee imported them and babied them to survive the summers), but there's willows EVERYWHERE. Everywhere there's water, anyway.
I've thought some along these lines too, but the only thing that keeps popping up going "yeah but" is that hot coil; some substances, and I'm thinking herbal essences, might not take kindly to all that heat. Not sure, to be honest. I know excessive heat would definitely render most vitamins inert, but I don't really know, for herbal decoctions. I'm also concerned about that direct application to the lungs that you mention; for some things, maybe slippery elm? that might be a great thing... other things, that are meant to act systemically, it might actually be toxic. One cold remedy I've heard of, and it does seem to work pretty well, is boiling rosemary in water, and hanging your head over it to snort up all those fumes... so rosemary might be a prime candidate, and maybe thyme; both of them are excellent anti-virals and anti-bacterials.
Andria