Comment
Names of groups and movements are known as 'proper nouns'. They should be given capital letters. Therefor:
Carrie A. Nation was involved with the Temperance Movement.
is correct.
The difficulty comes with the name itself. Is it "Temperance Movement" or "The Temperance Movement". If the latter, then "The" should get a capital letter by rights. There appears to be a lot of leniency on this though. Many people would not capitalise "The" because it looks too unwieldy.
