Some of the slightly smaller hp Mercs, 150V6 to name one, has a pair of thermostats, one at the top of each water jacket cover over the cylinders and a popoff valve located down, under the engine, I am told. A cooling outlet hose goes down there and it is probably at the end of that hose. My son had a 150 and I had a 90 3 cyl. I'll tell you about mine mainly and you can take it from there.
My pee was plumbed off the exhaust manifold cover meaning that I had pee anytime the engine was running, strength was rpm related since water pressure is rpm related. His was plumbed off his stat outputs. Easy to check that in that the cover over the stats (top of the left and right water jackets) had the hose connection as part of the stat cover. The starboard plumbed over to the port and the port went down to discharge the stat output water below the engine. His pee was teed off that hose....easy to see and follow. With that arrangement, you had to have the stat open to get pee, and it came and went as the stat opened and closed. Bad.
On the top of his engine block, between the banks of cylinders, aft of the flywheel was a hose the vented the engine block's cooling water (bubble eliminator if you will) and the hose went down below the engine block to the mid section.....I think this is where his popoff was located and was a separate system from the tstat system.
My 90, actually 75 thru 125 3 and 4 cylinder engines were inline engines and covered in my service manual. At the top of the water jacket cover at the rear of the block, was a cover with 2 bulges, one for the stat and the other for the popoff. The stat controlled the engine cooling (excluding the exhaust cooling part as it ran continuously) and opening temp was 143F which is right where a US domestic hot water heater thermostat is set when in the Normal temp position.....for a reference on how hot is 143. Son't stats were 143F also.
The stat controlled block temp till you got to around 2500 rpms which was just on plane for my boat running around 15-18 mph range. At 2500 rpms, (obviously that's a book number....in reality, in that general range of rpm) the water pressure produced from the engine pump and the ram water from the lower unit going through the water was enough to unseat the "popoff valve" which opened a much larger discharge port for engine cooling water, essentially bypassing the tstat if the ambient water + engine added heat was below 143F.
I bought my engine used. On my first outing everything was working ok, I was getting to know the boat as I bought it right and untested. I putted around for a few minutes in the harbor and started for the no wake buoys in the process of seeing what the boat would do. Before I got very far I got an Over Temp warning horn. Not knowing anything about the boat, I thought I'd hammer down on it and get some water pressure pushing on the water pump incase the impeller was shot.
I was running out pretty good for a minute or so and all of a sudden the OT warning quit. I completed my first ru with no problems and came back in, slowing for the buoys and within a minute or so, the horn came back on.
In short my tstat was frozen shut. The popoff bypassed it at the higher speeds and allowed the engine to cool adequately.
So, with what you have and what I said, "whatcha wann" to bet your popoff valve is stuck shut, just the opposite of what I had........ you can putt around but can't hook her up and run some rpms.
What do you think?