Who were the key figures in the the Temperance Movement?

I'm assuming you mean the American Temperance movement of the 19th and 20th centuries.  Temperance arose as a social issue because drinking was so widespread and socially destructive at the time, much more so than now even.

The Women's Christian Temperance Union formed in the early 1800s, with a number of people directly involved in the movement.  Mary Hunt was involved with a national education effort.  Lucy Webb Hayes and Susan B. Anthony, though she was a suffragist, were also involved in the movement.

Later the Anti-Saloon League formed and joined forces with the WCTU, including such notables as Carrie Nation.