A few people have tried after market filters, they didn't help mpg
Testing a 'performance' air filter for MPG - Part 2 - MetroMPG.com
I do think using
EXHAUST heat to offset throttle losses has possibilities , consider:
# At 0 °C and 100 kPa, dry air has a density of 1.2754 kg/m3.
# At 100 °C and 100 kPa, dry air has a density of 0.9336 kg/m3.
Not that all cars like hot air (possibly a software issue), but if yours does then if you can swing the temperature (about 100 degrees C just for example) as needed then you can basically "detune" the engine. Ok, so what you say.
Well the effects are compounding here. Your (gasoline) engine is least efficient with the throttle closed, if you are on the hiway and you are not quite at bsfc peak because of insufficient load for the engine, if you add heat, then:
1. the air going across the throttle plate and through the engine becomes less dense, therefore less restriction (1/4 less restriction in the example figures).
2. Because there is less air mass moving through the engine, you can (perhaps should) open the throttle more, reducing losses further for a given power output.
Now I have not thought enough about it to see if it affects peak bsfc rpm in a general manner, assuming an ideal ECU.
But as far as electric for heat, and why it is a bad idea, do the math, Here is your homework assignment:
1. Determine the mass flow of air you want to heat up (say, cruising the hiway)
2. Determine how much you want to heat the air
3. Determine how much power (amps*volts) you need to heat the air the desired amount.
4. Multiply that power by alternator/belt losses to determine how much power you are taking from the crankshaft (when exhaust heet is "free").