All overheats happen for one of 5 reasons, and these are the reasons from most likely to least likely.
1. Water is not getting in - bad seawater pump/impeller. Or a clog in the water line in the transom between the sterndrive and engine
2. Bad thermostat
3. Water is not getting out because of a clogged riser and or manifold
4. Water is not circulating - Bad circulation pump
5 Water is getting airbound - On some engines that can mean a head gasket issue, but that's not common with 3 liter engines. But what is common on the sterndrive is the water pocket grommet can dry rot out causing the copper water tube to have a very loose fit where it presses up in to the upper portion of the sterndrive.
That being said. What you want to do first is put the boat in the water. With the boat in the water disconnect the main water line that goes from the transom to the tstat housing and disconnect it at the tstat housing itself. Start the engine up and once the water starts coming out aim that hose into a 5 gallon bucket and run the engine at idle for 15 seconds, and then turn the engine off. In that time frame you should have at least 1.5 gallons of water. If you do not either the impeller is bad or the water pocket grommet for the water tube is bad. If you do get good flow, normally you would change the thermostat and retest, but you already did that. So step 2 would be to pull the boat back out. Then pull the exhaust riser off and see how clogged the riser and manifold water jackets are. Manifolds and risers are not lifetime items, and they do not last the life of the Engine. They all will eventually rust up and clog up. In saltwater this can be anywhere from 2 to 5 years depending on how often the engine gets flushed. In freshwater they last roughly 12 to 15 years before they rust up. If the manifold and riser are clean. The next place to go is the water pocket grommet inside of the sterndrive. Again when these fail air will get sucked into the water stream, and the engine block will get air bound. If that ends up looking good or still no change, then you would check the circulation pump and see if the steel impeller on the circulation pump fell off. (this isn't common at all, it only happens once in a blue moon, which is why it's the last thing to check). Does that all make sense. I do want to make sure you are happy with my service before you go. If you had a further question on the issue by all means feel free to ask. If not, Just in case you do not understand the way the website works (and some folks do not). You do have to put forth a positive rating in order for it to credit me for helping you. When ratings are not done, the website simply keeps your deposit and they will not credit me. The ratings box is located at the top of the screen. To rate, you must select the star you wish and also confirm it. Please let me know if you run into any problems or errors when trying to do it. If you do have a problem, or if you can not see the ratings box which is at the top of the screen. Please reply back "I rate Jason's service _______" and fill in the blank.
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Thanks in advance, and good luck