Gods, thermite, don't get me started on that bullshit.
Thermite is not used in cutting charges, it's easier, faster and safer to use standard plastic explosives than thermite reactions. Thermite is used in military roles as an incendary grendade, but the emphasis is not on cutting at all, it's to weld things. In fact to use thermite to cut through something you'd really want a vertical feed which kind of limits your application to horizontal bars, it might be possible to cut through vertical members with it, but i can't see how. I've seen thermite used to cut through a metal bar, you need a drip feed system to do so.
Also thermite is a thermally triggered reaction (note, reaction, not an explosion), you have to get it very hot to set it off. While conventional plastic explosives can literally be set on fire and used to cook your food (other than the toxic gases given off) thermite would be one of the most stupid choices for demolishing a building that's going to have large amounts of burning kerosene in the area.
It's also notoriously hard to set off, generally it's done by having a more reactive fuse fitted to it, magnesium for example. Electrical ignition is not used in any case i've heard of (although an ISFE would let you use a remote ignition system). Either way you run the risk of accidental ignition or failing to ignite at all.
Now, problems. If it were set off by the fire it would have gone a lot faster than the buildings really did. It'd ignite with the inital kerosene flash and take a matter of minutes (very few of them) to burn through the support members.
The entire idea of thermite being used is based upon the same intellectual laziness as the idea the the WTC 7 building was demolished. Seeing something and then leaping to the first conclusion that you like the look of. All we know is that there is signs of intense heat in the building, we do not know the cause and we do not know the exact temperatures.
There is no reason to use thermite to demolish the building, it's inefficent, difficult to control, more sensitive to thermal issues than plastique and inappropriate for deomolition.