it was solved repeatedly by the tuner scott siegal @ topspeed...
they recorded temps 20* colder with the cold air intake.
When the hood is up/open on the dyno is doesnt do much, but in actual driving conditions, when the hood is closed the CAI runs on average 20 degree's colder...
remember, HP Output = +1% HP per 10 degrees
for ex. 300whp car is going to gain 6whp on top of the SRI
On any forced induction engine where you are compressing air and pushing it into the cylinder (instead of the cylinder's vacuum sucking the mixture in) you will not see equal temperature reduction from a CAI post-boost like you do pre-boost.
A simple example would be:
N/A car with CAI; IAT's drop 20 degrees; Engine coolant temperature is at 200 degrees; Ideally, based on a lot of assumptions*, you would have about a 2% increase in power.
Turbo car with CAI; IAT's drop 20 degrees; Compression at the turbine heats the air to 70 degrees over your IAT's; Intercooler cools the boosted air 50 degrees; Once finally pushed into the cylinder, boosted air is 20 degrees higher than the IAT and you have effectively seen nearly no improvement.
* The rule of thumb that 10 degree reduction equals +1% power is an educated guess at best. It gets thrown around a lot and associated to situations it has nothing to do with. Many people assume that it's based on engine coolant temperature. For example, subtracting 10 degrees off your coolant temps by using a more efficient radiator. Not so much the case.
Your coolant temperature may be 200F, but your engine is running much hotter than that. The assumption it is based on coolant temps makes assumptions that there is no energy loss (radiated heat). If you were to eliminate your radiator and run the engine long enough, there will be a point before it overheats where you will see just how hot the engine runs. The whole engine is not the same temperature, which is another assumption made with that rule of thumb.
Essentially, the 10 degrees reduction from true engine temperatures is rationally a much smaller increment than it is from coolant temperatures. So someone who assumes this assumes they are gaining much more than they really are.
For intake air temperatures (IATs) on a naturally aspirated car, a 10 degree reduction will see some increase in noticeable power. The air mixture versus fuel in the cylinder is more dense (more parts oxygen versus gasoline); and the cooler air/fuel charge is helping keep cylinder temperatures slightly lower which reduces the chance of detonation. Both of these things allow you to advance the timing just a bit more and make more power.
The argument that just because you lower your IATs by 10 degrees you got another +1% power is fallacious unless when making that argument you show that you have seen the task through by way of advancing the timing. At that point, you should just say "I lowered the IATs on my car and was able to advance the timing and make a bit more power". Also, another thing that should be noted is the rule of thumb was based upon flywheel horsepower, not wheel horsepower. Knowing this, you can see where "a fraction of a fraction of a fraction" doesn't leave turbocharged users much to gain with CAI for this particular platform.