Welcome to the forum.
My guess is that you do not have a T-stat at all. Not to worry. There are many set ups that will work. This post may help
http://www.moyermarineforum.com/foru...ad.php?t=10248
The only way to tell is follow each line and let us know where it goes.
Can you give more info on all the lines running to/thru the muffler, and I assume you are referring to the red part in the second pic, and the valve assembly? Does the "uphill" black hose come directly from the manifold? Is there only one hose leaving the manifold? What exits the muffler and where does it go. I think I understand your set up from your first post but just want to clarify. Some folks have set up a system that allows them to divert some of the hot water coming from the manifold directly overboard and not send it all thru the muffler ect. I believe this is designed to reduce the exhaust system back pressure. You do not have to have full water flow to keep the muffler and exhaust hose happy.
Your system may be a modification of a modification.
Dan S/V Marian Claire
Edit: Another thought on the valve is that it could be a way to by-pass the muffler and wet/dry connection altogether. This would prevent water from backing up into the cylinders if she does not fire up quickly. Any history of water in the cylinders? Reason for rebuild?