This is actually quite normal and nothing to be concerned about. If the engine temperature is high enough, the computer will continue to run the cooling fan even though the ignition has been turned off. This helps keep the temperature from spiking when the vehicle stops and is turned off.

Even though this only really lowers the temperature of the coolant in the radiator (not in the actual engine) it also helps to maintain a constant, safe temperature if you restart the car soon after shutting it down.

That said, the fan should only continue running for a couple of minutes at most after you’ve turned the car off. Any longer and you might have a problem with the circuits that power and control the electric fan.

A common cause of overheating can be a failed head gasket which allows the coolant to be consumed by the engine. When this happens, soon there’s not enough coolant remaining to cool the engine and the car overheats.

But it may not be as serious as that. You could simply have a stuck thermostat. This is the component that prevents coolant flowing around the engine when it’s first started, forcing the engine to warm up faster. Then, as the engine gets warmer, the thermostat starts to open to allow the coolant to flow through the engine and do its job, maintaining the correct running temperature in the process.

Other possible causes for overheating include incorrect ignition timing, a slipping fan belt, non-functioning cooling fans, a collapsed radiator hose, blocked radiator, a worn water pump and many others. A good mechanic should be able to make a diagnosis and tackle the problem from there.

A cracked turbocharger intake pipe is a pretty common problem as this tubing has to withstand high temperatures and the force of the turbo’s boost. You really wouldn’t bother trying to fix this, and a replacement piece of tubing is the proper fix.

Just make sure you get the right piece of tubing as there are different pipes of different shapes that run between the turbocharger and intercooler, and the intercooler and the engine. It’s quite possible to change these yourself, but modern engine bays can be pretty tight and you might find it’s a fiddlier job than you imagined.

While you’re in there, check the condition of the clamps that secure the tubing, too. You may wish to replace them at the same time. I’ve seen replacement pipe kits for anywhere from $200 to $300 for this make and model. Online sellers are plentiful, but conventional parts stores should also be able to help you out.