The tube from the airbox to manifold is two piece (accually three with the box looking affair that will be removed). I just removed the heater or "warming" box from the path, hence "cooling" or in reality keeping the air cool. The box thing lays really close to the exhaust manifold and I'm assuming it's Toyotas way of pre-heating the incoming air charge...why, I don't know, but I looked at it as defeating the "cold air" intake. So the solution was a tube/path away from the manifold.
Simple rule of thumb I use, gained from an engineer at BDS superchargers is this...for every 10 degree drop in intake air temp...it's one free horsepower. Without getting into air density/moisture and other issues involved...suffice to say that the colder the incoming air, the better...which is why we use "cold air" kits, intercoolers, etc.
Something to also keep in mind...instead of using header wrap, which will accually damage the manifold/header, consider ceramic coating(s). The initial cost of ceramic may seem expensive, but by the time you buy the wrap, destroy the part, then have to replace it...and then coat it...it's pretty cheap. The theory behind coating (or wraping) an exhaust component, is to keep the air inside the header (or whatever) hot, and therefore easier to move...not so much keeping the air around the component cool (although in a hooded vehicle it's a bonus) Cast iron manifolds are more suseptable to damage than tube headers because of the type of metal (cast versus forged or drawn) The heat contained within the wrap, will burn a certain ammount of the carbon out of the metal, create fatigue, and eventually break.
Anyway...i'll get some photos and let you decide.