Engine over heating

Just bought a 1968 Evinrude Rogue with an OMC stringer outdrive and a Chevy 307 V-8. The boat runs great for about 20 minutes and then the dummy heat lamp comes on. I have checked the impeller, pulled the inlet hose from motor to manifold and manifold to thermostat and all are getting water as well as water exiting out of the back of the engine. This engine has two hoses coming out of the manifold and entering the thermostat as well as two coming out the other side of the thermostat and going to the manifold on the other side of the engine. The curious thing here is that the two lower inlet/outlet hoses are both cool to the touch while the two upper inlet/outlet hoses are not. The inlet hose on the upper is cool as a cucumber while the upper outlet hose exiting the thermostat is hot, hot, hot.
In addition, after I shut the boat off, it only takes a few minutes to cool down, it fires right up, runs great under 2000 rpm. No smoke or burning smell. Usually just head back to the dock and tie it up. Any help would be appreciated.

could be a thermostat
could be the impeller sucking exhaust gases underway - the remedy for that is to grease the swivel housing - the grease zerk is inside a hole in the cavity of the drive - front side of the exh housing of the outdrive

Thanks for the reply hystat. I suspected the thermostat. However, never would have thought of lubing swivel housing. Can I reach the grese zerk with the boat in the water?

yeah, I suppose...maybe put your grease gun in a heavy plastic bag, or join several long whip lines. but never join grease lines with cast plumbing connectors rated for 200 psi. Grease guns can make 10,000 psi in the hands of a strong person. need seamless steel unions designed for hydraulics.

Hystat, just a quick question. That zerk on the front of the drive, when do you know the proper amount of grease has been put in it and what is that grease doing to stop exhaust gas from coming back into the water intake. I just finally got grease into that fitting, had to get and extension device to even get to it, head of grease gun, even mini one, were all too big to go into zerk hole deeply enough. Thanks! - G

Still working on over heating problem. This is what we have done thus far.

1. New thermostat
2. New impeller on water intake
3. New impeller on engine mounted water pump
4. Adjusted timing.
5. Cleaned and flushed out fresh water intake.
6. Verified flow through all intake and out take hoses.
7. New 14 x 16 prop and prop bushings. (Not replaced as a fix to over heating, just needed it.)
8. Greased the swivel housing.

The boat still over heats after about 10 minutes running at around 4500 rpms. Next on the list is to pull the exhaust manifolds and see if they are clogged. Any other suggestions would be helpful.

pull the risers, they might be clogged. You may also have flappers. Or used to have flappers.