"What happens exactly that they're concerned about?"
From a purely mechanical (non-electrical) temperature related issue: Heat soak
When you are running an air cooled engine (anything really) at high power loads, the engine is generating maximum heat/power. When you shut it down without a cooling period, the cooling systems stops, abruptly. However, the cylinder head, piston(s), exhaust valves continue to shed heat to the cooler parts of the engine without an operating cooling system. The oiling system is also shut off. Under some conditions, the engine oil, which also serves as coolant, especially in an air cooled engine, can overheat and coke. It doesn't happen all at one time/overnight, but over time, many an air cooled engine, especially with turbo chargers, overheat and burn the oil up creating sludge which can eventually kill the engine/turbo.
Many auto manufacturers of the late 70's and early 80's learned their lesson BIG TIME with their turbo charged cars that weren't equipped after run cooling systems. Premature turbo failure (under factory warranty) was common because owners typically shut the engines off without a cool down period. This eventually led the big push to modern synthetic oils which could handle higher temperatures without coking up.
My first boss had the habit of chopping the throttles on his Cessna 310 (twin air cooled engines) when descending from 12,000 feet @ 65% power at well below freezing. As a young pilot with more mechanical knowledge than flying time, I told him that was a bad idea. He laughed saying, "Naaahhhhhh, it's fine, I do it all the time." He stopped laughing when he got the $25,000 bill for multiple cracked cylinders/pistons/exhaust manifolds. He was lucky to make it home safely. For engines, shock cooling/heat soaking is NOT a good thing.
Chum lee
