Jeep Strokers

Is hot air or cold air better for fuel mileage? The reasons I am asking is because i have been thinking of installing a vacuum valve (maybe a supercharger bypass valve) to pull warm air from the engine bay for better mileage when cruising. The valve would close when vacuum drops. However, I would also be concerned about when the valve does close would the hot air heat the intake enough to warm the now cold air?

I would imagine that hot air would do better for mileage, the IAT would sense the cold air and richen the mixture due to the cold air?, colder denser air/more fuel, more power, less economy?
You can probably better effect your economy with stringent modulation of the skinny pedal, but that aint no fun!

ill say the same. i noticed with my cold air intake (a true cold air, filter in the fender, away from engine bay heat) on my old honda, my mileage took a massive shit in the winter time, even considering warmup time

That could be some explanation of why my Scout gets 18MPG?, it sucks HOT under hood air in the summer time and SMOKING HOT! air off of the exhaust manifold in the winter time?

the dip was more dramatic after the intake was added

warmer air is better for fuel economy because it promotes vaporization prior to ignition... less fuel goes to waste.
also if the incoming air is TOO cold.. the fuel may have tendency to condense slightly on the cylinder walls prior to combustion, until the engine warms up FULLY.
the proximity of the intake to the exhaust on the 4.0 allows the charge to get warmed up nicely before entering the cylinders...
don't mess with success !

do you have a scangauge or other method to actually measure the IAT sensor directly?

the reason I ask is because I see between 80°F to 180°F IAT's with my Scangauge, with temperatures ranging from -10°F to 100°F. the engine compartment does a good job of warming the intake tube already. keep in mind you're only sucking in cold air when you have the throttle body wide open for an extended period of time. if you're at partial throttle, the air in the tube is moving slower and has more time to heat up before entering the combustion.