Ok lets examine this a bit here. Cool air is more dense than hot air thus there are more O2 molecules for cumbustion. Getting cool air from the outside is important for this reason.

Cool air is also important for another reason. To prevent detonation. Thus the intercooler. It cools the air to enable more boost (either supercharged or turbocharged) without detonation with the same octane fuel.

Once the air has passed through the turbo or blower then cooling it for the purpose of making it more dense is seemingly pointless. The charge of air in the intercooler is already set before the air is cooled. Making it more dense will not create more O2 molecules.

This leaves the other reason. Enabling more boost. Unless the lightening has a blower or turbo with a means of increasing boost rates when this cold air is put through the intercooler to take advantage of it's increased ability then I don't see much benefit to it in this capacity either.

Maybe the timing can be advanced some during this time to create more top end power. This would be possible with computer controlled timing. The knock sensor would register less detonation due to the colder intake charge thus enabling advanced timing.

I doubt if this alone would increase HP by 40. I would be interested to read more about this. Does anyone know of a link detailing how this works?