Sounds like utter nonsense to me:
Gas mileage depends on lots of things like vehicle weight, air drag, tire rotational drag, rotating friction, viscous friction of oil in bearing surfaces, combustion efficiency, and of course driving technique. It has nothing to do with the properties of the metal in the engine -- except perhaps how light the engine is. From a mileage point of view a really light engine that wore out in a hurry would beat a heavier engine any day.
Even if some heat/cold treatment actually changed the properties of the metal in the engine it would make no difference in the gas mileage of the car. It might have some effect on the longevity of the bearings, or cylinder bores, for example, but it wouldn't change the mileage.
Of course chilling the gasoline itself might be a way to increase the apparent mileage -- the cold gasoline would be denser so you'd get a little more in the tank...
Maybe the Laws of Thermodynamics have been repealed.
Seriously, no one should get a degree in Journalism without 3 semesters of physics, a couple of hours of chemistry, and a course or two on thermo and heat transfer.