I've only used black screens for that type of keying (Smoke and fire) and it's pretty easy, especially since you can use a blending mode in 1 second instead of taking the time to key it. I've always assumed a green screen wouldn't work as well.
I'd use a black model resembling the shack to set on fire, and superimpose that video on the real shack. That could be done pretty quickly too, so it would be worth trying even if you do end up building a miniature replica.

Just on the cg side of things. Maya has built in fire samples. They are ok, but if its a daylight scene the fire wouldnt look so good.
The best cg fire at the moment that isnt proprietary software is probably fume fx.


FumeFX fireball on Vimeo

fumefx flame test on Vimeo

FumeFX burning wood log - HD on Vimeo


I think the black screen compositing method is used a lot in professional fx. You can also get stock clips of fire and smoke form online sites for this purpose.

I'll put in a second for FumeFX, but it's not easy and you need 3ds max for it. Check out the 'sample A' from this training DVD:

ALLAN MCKAY - FUME FX ADVANCED DVD