The subframes are pretty far away from your interior and the carpeting is fire resistant. They'll smoke significantly before actually going up. There is really minimal welding involved with the SFC install. A good welder is going to do a lot of area prep to get it to bare metal, tack the key places and run 1" or so stitch welds, moving constantly. There really isn't enough time or proximity to build up enough heat to go through the subframes, into the floorboards, and heat up the carpet to the point where it will catch fire.
It doesn't hurt to have a second person watching the carpets with fire extinguisher handy, though.