Short answer
First establish whether the engine reaches its rated maximum rpm. If it cannot, the boat is overloaded and heat is a symptom, not the fault. If it can, the cooling system has run out of margin: check raw-water volume, heat exchanger condition, exhaust restriction, thermostat and coolant level.
You will need: Tachometer or engine display, infrared thermometer, torch
Overheating that appears only under load is a margin problem. The system copes at low heat output and runs short as heat rises, which narrows the search usefully.
Start with the one measurement that splits the problem
Run the engine up and note the maximum rpm you can actually reach at full throttle in clear water. Compare it with the engine's rated figure.
Cannot reach rated rpm: the engine is overloaded — a fouled hull, a damaged or wrongly pitched propeller, or a boat carrying more than it used to. The engine is working harder for the same speed and producing more heat as a result. Fix the load, and the heat usually goes with it. See propellers and engine load and improving efficiency.
Can reach rated rpm: the load is right and the cooling system is short of capacity.
If the load is right, work the cooling side
- Raw-water volume at the exhaust, at load, not just at idle — see how to check raw-water flow.
- Heat exchanger fouling or scale, and aftercooler where fitted.
- Exhaust restriction at the mixing elbow, which builds up over years.
- Thermostat, coolant level and concentration, trapped air after recent work.
- Belt tension and pump condition on the coolant side.
The safety line
Rapidly rising temperature, steam, loss of exhaust water or a burning smell calls for prompt action: reduce load, assess whether shutdown is safe, and never remove a hot pressure cap. See emergencies.