One could argue that hot air will call for less fuel , this is true, but it will not result in increased fuel mileage. The hot air, we are talking about, 180 -200 degree coming off the radiator, heats the intake tract to roughly the same temp, the amount of air over the outside being so much greater than the internal flow. This is outside the range of the MAFS, so it results in a slightly rich weak mixture on the low side of the stoichoimetric ideal. Low air density also impedes volumetric efficiency as the engine wants as much air as it can get as freely as possible, resulting in better combustion chamber swirl.
if you want hot air, you need it really hot, about 450 or so, this is called a plasma induction system, Smokey Yunick developed it in the 70's, it used two turbos, lots of boost and was really efficient. and the metalurgy it needed was expensive. It it also needs direct injection otherwise you get an exothermic reaction ( detonation). Another problem caused by hot air intake tracts. So keep it cool and spend less on fuel.