The best way would be to have two intake channels and shifting between them depending on the power requested.
This was standard equipment on GMs in the 1980s (and I think 70s too). Called Thermac, it used vacuum and an air thermostat to control a damper that mixed intake air from the snorkel or the exhaust manifold stove. Granted, that snorkel was still pulling warm underhood air in a lot of vehicles, but some were piped to a CAI...mine is now. When vacuum got below 5 inches, the damper would close the hot manifold air and open the snorkel air instead of mixing thermostatically.
OT; theholycow: Ok, so that's how it's implemented. My brother has this in his Silverado 2500 truck -91. But the "throttle" has jammed in the closed position only taking air from the exhaust manifold stove. He took the lid off and replaced the air-filter instead to an open aftermarket filter. Not the most FE car to start with anyway.
HAI was explained to me simply as "hot air helps atomize fuel better, reducing the amount the injectors need to spray" so I understood that by adding hot air to the intake air, the fuel would burn more efficiently, and I'd use less gas pedal to move forward, but as mentioned, at the expense of horsepower taking a small drop.
Now that could be completely off, but I do know that depending on your car whether it's MAP equipped or MAF equipped, using a HAI works or it doesn't. MAF cars sense the incoming air temperature and the computer recalculates fueling to maintain optimal levels, MAP cars (like the S-Series Saturns) cannot do this, so the computer cannot alter fueling based on intake air temperatures... so fabbing a HAI and feeding the engine 160*F air effectively increases efficiencies beyond what the computer can adjust for, and you increase FE.
My previous car had MAP-sensor and IAT-sensor, that is why it was possible for scangauge to calculate the fuel consumption because you need both these, engine displacement and a scaling constant. I would think most modern cars have an IAT-sensor.