No, thermite can't, it’s too hot to be directed, it will melt anything trying to direct it. Second, the vertical beams are the load bearing beams, not the vertical beams.
Sorry, you are flat out wrong on this, feel free to argue shaped charges, they are commonly used for controlled demolitions, but thermite is not used for controlled demolitions, because its not controllable, it burns straight down, its only good for welding railroads and putting holes in cars.
Here is the best known attempt to direct thermite
http://www.itep.ws/pdf/FOI_Rapport.pdf
It failed, and at best, it could direct a small amount to cut a small hole, not an entire beam. Thermite is flat wrong.