This is called "dieseling" and is a bad thing. There are several reasons it might happen, but the short answer is "take it to a mechanic, tell him it's dieseling, and let him figure it out."
Check your timing and if it is a carb, check to make sure the air fuel mixture is set properly.
Several things can cause this phenomenon, called dieseling. Built up carbon in the cylinders, incorrect timing, an overheated engine, a lean carburetor setting, or a fast idle can all be contributors to dieseling.?æ
There are many possibilities. More information is needed. If it's a 70's era car that's dieseling, could be the timing is off, or the anti-dieseling solenoid isn't working. If the car has had an electric fan installed recently, and won't shut off when the fan is running, the fan is not properly wired. If it's a computer controlled car, could be a problem with the ignition switch or ecm.
If it runs fine, probably an Ignition Cylinder problem If it runs kinda funny, probably it's just "dieseling"
That's called dieseling, and the main thing that causes it is improper ignition timing.
You did not specify make model and year. If you have a very old car It could be doing what is called dieseling. OR The engine computer could be keeping it running to try to get it to cool off. But with out knowing what car it is those are just guesses.
The fast idle solenoid
The braking system makes a car stop.
the solution can depend on the year and induction type. usually too high an idle speed and rich idle mixture combine to allow a hot carbon chunk in the cylinder to ignite the mix and cause the dieseling. on injected engine its far less common but leaky injectors have been known to cause the condition also
If by "stop the engine", you mean turn the car off, then the answer is NO!
You should stop your car just before the line, ensuring that no part of your car crosses it.