In every Mercury I have owned or gotten into with a thermostat, the pellet was stamped 143F. I understand that there are some engines running 120ish stats but I haven't been around them. The mid position, normal setting for a US domestic hot water heater in the home is 140F for a reference point. Since you are at 40 hp you probably don't have a high speed bypass valve so the engine block should remain at least pretty warm to the touch while operating.
Years ago Mercs had no stat and it wasn't until they decided to upgrade molds and all that, reduce the cylinder count for one thing in multi cylinder engines, give everybody a thru hub exhaust and all that that they brought in tstats. Their advertising was around the high intensity, fast rising spark to get the plugs fired before the charge could leak off due to moisture or combustion contamination. OMC (Johnson-Evinrude) had stats way back in the 50's.
No doubt that the stat is part of the combustion process. The automotive market has incorporated hotter and hotter engines in the quest for lower emissions.....aka cleaner, more complete combustion. They sell them (stats) on here....look at the top of the page under Boat Parts and Accessories.
You don't supply a complete history of your engine so any answer to your question is purely speculation. There are things that are suggested to correct normally found problems but they may not apply to your situation.
We are in the middle of winter here and cold, damp, conditions on possibly seldom used engines, especially of vintgage origin, with today's fuels, sitting around with old fuel and all are certainly a problem.
With all that said, I personally would check fuel first as the culprit while you are locating a new tstat for your engine. The fact that you said what you did tells me that you had some crud floating around and your initial satisfactory operation dislodged it from where it was and deposited it where it shouldn't be. If you never run your engine out at Wide Open Throttle (WOT) or spend a lot of time idling, or trolling, you can expect things to get clogged up, especially on cold days with old fuel. One thing I liked to run in my fuel was Sea Foam which cleans the whole system and is perfect for 2 stroke outboard engines. I ran it in every tank and kept reasonably clean fresh fuel in my tanks and just didn't have fuel related problems due to bad fuel or the like.
I think you need to install a carburetor kit and in the process do a complete clean out of it in the process. A good soaking in Berryman's chem tool, then manual cleaning of all the ports and holes, and tubes and all in the process. A thorough blowing out of all the ports with 100 psi air when finished, will certainly not hurt. A fresh tank of fuel mix with cleaning out the fuel lines in the process won't hurt. Then we can go from there. Let us know what you find.