Didn't have to melt the steel for it to fail.
The steel in the floor trusses softened enough for them to begin to collapse.
http://www.popularmechanics.com/science/defense/1227842.html?page=4&c=y
It's worth noting that besides the weakening of the steel at high temperatures, that the steel also expands significantly. This places huge undesigned-for stresses at the connections (like where beams tie into columns). You get a failure going on one beam, weight gets transferred to the adjacent beams, they fail, etc, and the whole thing comes down.
Correct, it was not so much the columns fialing, but the floor decks/trusses that brace the perimeter tube failing. As overstressed columns began to have their lateral bracing destroyed(the floors braced the perimeter), the perimeter tube finally buckled and the building comes down.