It is thought that the Freemasons (one of whose subsidiary organizations is the Shrine) derive from the Templars.
My understanding (and very limited) is that the Shriners broke off from the Masons who they considered too uptight. They wanted a group with more fun.
To my thinking that disassociates them as they wanted their own group away from the traditions of the first. But I may have that understanding distorted. I see them as a new group, not a continuation of the old.
That is science fiction, according to a real history of the Templars:
http://www.amazon.com/Templars-Piers-Paul-Read/dp/030681496X
The Templars by Piers Paul Read