Looks like other tool fans have been wondering about this sort of tool too: http://toolmonger.com/2011/07/22/questionmonger-what-is-this-tool/
From the answers, it appears to be a pinching iron for curling wigs. It would be heated on a stove. The Round area is for retaining heat, and the hair is straightened or curled between the flat portions. As a wig making tool, it would need to be fairly delicate, and the extended finger guards would allow it to be operated easily with one hand.