One thing to remember about air-cooled engines, especially stationary ones, is that they are designed to run at their designed rpm, not only for max HP, but to cool properly.
If the engine is a 10HP and that is at 3600rpm for example (common rpm for singles), it should be run at that speed so the fan on the flywheel can blow enough air across the head/cylinder to cool it properly. Heavy work at lower RPM, such as mowing heavy grass, will cause the motor to run hot.
Also, they don't idle down low like a car. They idle high to keep cool, and splash lube models need to splash enough to lube properly. Many of these engines are quite simple, and are designed to operate in a short operating rpm range.
Not trying to be smart, just something to think about.