The above is generally true especially for regular cars; but there are exceptions when the critical components depend on active cooling to dissipate the heat.
So the answer to your question depends on what your definition of "engine" is. Exactly where you are measuring a temperature, there are definitely components that gets hotter after shutdown. If you are defining the engine as the combustion chamber where it's 2000 degrees or whatever, then yes it's not going to get hotter than 2000 degrees, if there are no more burning of fuel in there.
Real Life common examples that show this :
Turbo cars, especially modified ones, utilize idle timers to let the turbo cool down before completely shutting down.
Race cars also have to take a cool down lap, they don't just shut it down right at finish. In F1, when they can't take a cooldown lap, they have to stuff blowers onto all the intakes so the heatsoak doesn't damage parts.
Or, if you have a video projector, when you turn it off, the fan keeps going for some extra minutes to prevent the lamp and components from overheating from the residual heat