Curling is a fascinating sport and I was sent this link (I forget by whom) that says that the way the stone veers as it moves along is a bit of a puzzle for physicists. (If the embedded video below does not work, follow the above link.)
I would be wary of the friction-caused melting theory because as I said in a previous post about why ice is slippery, that explanation is not tenable. I had not been aware that the ice surface in curling are prepared is such a way as to produce tiny bumps on the surface of the ice. I suspect that that it the most probable cause for the unusual behavior, though the precise mechanism is not clear.