Temperature rise a motor after shutdown

What you see is true - no crazyness detected

There is no specific phrase which I know of but try googling things like "Thermal Lag", "Thermal Over-run", "Thermal Peaking". There are likely some industry-specific terms.

This phenomenon is why car radiator fans keep running for a few minutes in hot weather after a hard drive when you switch off , get out and walk away. They are designed to do it - I noticed French cars are very keen on doing this.

gwolf

The core temperature does not increase after engine shutdown. The hotest parts of the engine are the cylinder heads and pistons and they are hottest while the engine is running. These are much hotter than boiling water. When you shut the engine off you lose water circulation and the water in contact with the hot engine parts will get considerably hotter than when there was circulation. This water will boil and push water out of the radiator cap.

If you turn the heater on in the passenger compartment that will usually prevent overheating of an idling engine.

Yes, but the temperature increase you see is registered by whatever temperature gage is installed - and these are almost universally WATER temperature, not block temperature.

For a water cooled engine to work the water temperature inside the block - at steady-state operating conditions - must be lower than the jacket temperature. It it wasn't there wouldn't be any heat transfer.

The water gets lower by passing through the water-to-air heat exchanger commonly referred to as a "radiator".

When you shut the engine off you also shut the water pump off.

Heat from the jacket still transfers into the water, but because the water is no longer circulating it can't reject the the heat, so it has to get hotter. The block meanwhile is getting cooler.

Eventually the water and block temperatures equillibrate, and the both will start to fall.

The total enthalpy in the engine/coolant system can only decrease after the the engine is shut down, but the temperatures of different parts of the system may increase.

The heat from the (usually heavy cast iron) exhaust manifolds is usually the problem on shutdown, especially after high -load operation. This heat soaks back into the cylinder head and, depending on relative thermal inertias, could heat the head (or parts of it) above its usual operating temperature (this is also what cokes the oil in your turbo bearings). It can also boil the coolant locally, causing hot spots and warping of components.

I had a Honda with a faulty fan switch and I drove it around for quite a while before I realized it was broken because I don't idle my vehicles long.