It could be something as simple and inexpensive as the radiator cap. They're supposed to seal from the factory, and many of them do, but sometimes not for very long, and not at the pressure they're supposed to be rated for. When you turn the engine off particularly after running it relatively hard, it is going to heat soak and the pressure in the cooling system will actually rise: there's nothing turning the water pump, there's no air flowing through the engine compartment, and the exhaust manifold(s) are still HOT, as are the cylinder heads, particularly around the exhaust valves. Remember, too that a lot of new cars are designed to meet very stringent emission requirements - which means those catalytic converters are CLOSE to the engine compartment and exhaust manifolds for fast "light off" and they get *very* hot. The result is many, many BTUs of thermal energy that have to go somewhere when you turn off the car. The first place they try to go is the cooling system.
If the cap is marginal or defective you can smell it, because the coolant boils off and escapes past the seal.
Early turbocharged Audi Quattros had an "after run cooling pump" that actually had its own thermostat and switched on when the engine was turned off, to pump the coolant around and keep it from boiling because of the latent heat from the turbocharger and exhaust manifold soaking back into the engine block. Some of those turbos and manifolds would get so hot that you could open the hood in a dark garage and see them glowing dull to bright orange, particularly if you had just run the car hard. About 20-30 seconds after you'd switch off, you'd hear the after-run coolant pump start up, and it would stay on for several minutes in some cases. In extreme cases even the electric cooling fans would continue to run during the whole time, and in fact they would switch to higher speeds to dissipate the heat. So you'd shut the car off and 1 minute later it was howling in the garage like it was still running. This is on a 100% stock, "from-the-factory" car. Glowing exhaust manifolds and turbocharger and I've seen it many times.
If the rest of the cooling system wasn't sealed, particularly the radiator/reservoir cap, you could smell it **right away**. You could hear it boil. The reservoir cap was a pain, and sometimes the reservoir itself *cracked* from the pressure and temperature of the coolant. In fact that was a major headache on the early Turbo cars: cracks in the coolant reservoir, even with the after-run pump working perfectly. The post-shutdown heat soak temperatures and pressures were so high sometimes that they just overwhelmed the thick plastic coolant reservoirs themselves, nevermind the caps.
This isn't a turbo car, but a poorly-sealing radiator cap can mimic a much larger problem. So look there first.
Good luck I hope it's something simple and inexpensive like that. It could very well be.
