Depends on how hot the thermate slag is. If the drips keep coming they could do what we see. This is a possibility.
The potential chemical energy per gram of mass stored thermate is surprisingly low - much lower than that of most organic combustibles found in office buildings, such as paper, wood, paints, plastics and many fibers. (
ETA: btw., That's why the Harriet/Jones paper conclusively proves that the red/gray chips are NOT thermate: By their own data, they chips release more energy than thermite of any kind contains. Then again, I have to add a disclaimer here: paper would
prove this conclusively, if the method used had been valid. It wasn't. So really the paper proves nothing except that its authors are incompetent /ETA) Since the thermate reaction releases no gas, it reaches its extremely high temperatures. However that heat quickly dissipates through radiation.
ETA: In other words: The thermite reaction produces very high
temperatures locally (i.e. the reactants themselves get hot for a brief moment), but produces much less
heat than conventional combustibles. Therefore, to reach the same
sustained heat at a certain volume (say, a steal beam, or a trash heap), you need a lot more thermate than usual office contents. /ETA
How much thermate slag would you need to heat a steal beam to the required temperatures, given its low content of kJ/g, how could it have been places, and would it not have melted any materiel it was attached to while it burned? Why was no resolidified steel found anywhere in the 3 rubble piles?