Yes, sucking in hot air will improve your gas mileage... but at the cost of power and potentially causing detonation. Ever notice how your gas mileage goes up in the summer time, and is crappy in the winter? In the 97GT, I could normally get 24-25mpg during the hot months of summer, and it dropped to 19-20mpg in the winter, with the same driving habits and route.
Hot air will better atomize the fuel and help more of the fuel vaporize as it is going into the cylinder. Of course, better atomization and mixing results in a more complete burn for better efficiency. Another effect may be causing the engine to work harder and reducing the losses from throttling. An engine working harder is more efficient (long as you don't go to open loop).
So yes, your mileage will be better... but you are going to loose a lot of power unless design the system to suck in cold air at full throttle. Also, hot air is more likely to cause detonation. Most modern cars will reduce the spark timing to prevent detonation when they see hot air, which isn't helpful for gas mileage.
On a side note, my 88 2.3 had a ford factory origional system to suck in hot air in certain conditions. It had a metal sleeve around the exhaust manifold, with a tube going to the air box. There was a vacuum controlled door which could open and supply the engine with pre-heated air from the exhaust manifold. I think it was mostly used when the engine was cold, to reduce emissions. And yes, I lost mileage when it was removed.
