A lot if the posts are about simple change of air filter - not a cold box
as I have always had them as difefrent.
To me sports induction is getting more air in and if it is in the same place (as most filter systems are) its not a cold box.
A cold box is only any use when you are producing a lot of heat - normally turbo engines on high boost . It also works best with some sort of "ram" air intake to make sure the air is cool
And if you change the filter for the sound thats definately NOT a cold box .
Absolutely fine to do (if thats your thing ) but not a cold box.
In my experience you get better result's with a Na engine when installed properly.
With a turbocharged engine the temps will on go as low as the intercooler will let them.
To lower intake temps on a turbo you fit and IC spray or something as fitting a CAI will do just about nothing to a turbo engine in terms of intake temps.
I agree with you sleeper, the colder the air enters the turbo if the same amount of energy is used to heat it up, the cooler it will leave the turbo. I don't think it's AS important as in an N/A car (due to intercooling) but the more boost and power you are running the more important it becomes imo.