You are correct, any part that stays in the engine bay (static) will become heat soaked. The air traveling through those parts, however, is not static hence the pot pie/oven comment.
I respect the amount of time and effort you've put into this but I just don't see a great potential for benefit when it's all said and done. Just my 1.5 cents...

I looked at the cold intake option, and I made this decision which definitely helped my engine be cold-style responsive during long trips:

I purchased thick aluminum heat resistant tape and covered the whole section from air box to throttle body. Since this mod, I never see this part hot anymore. I believe this makes a difference for the engine, based on personal observation.

Honest question here, I do not understand how the engine is going to suck up more air. Yes the filter can be as big as you want but unless it is forced induction, the engine is not going to suck up more air regardless the size of the filter, unless I am missing something?

What is "be cold-style responsive during long trip"? Outside of air temp or component temp that you say it is cooler, I am curious what exactly is your personal observation here that makes a difference for the engine? Improved gas mileage? Faster acceleration? Quieter engine at cruising?

I'm not trying to start a war here but I would be surprised if ANY intake design would give more horsepower than the stock one on a 3uz. It's already a cold air intake design with "ram air" provision. This is a pretty low revving, low rpm car that doesn't demand too much air in the first place, and the stock air filter size is pretty large.
What I am very surprised about is how much power some good headers will add though -- multiple dynos proving 20wrhp! To me that is more understandable if you look at the stock manifold design vs the SS headers.

Best would be to realize what these cars are and that a Pontiac G6 will run right next to you and a V6 Camaro two generations old will outrun you with ease. These are slow cars, the point was never speed it was comfort and luxury. If you want to go fast get something with an LS1/3/6/7

I am 100% positive my set up gets more air to the car than the stock intake there is a 5x12 duct ramming air through to a 4 inch opening then a 4 inch to 3 inch reducer to 3 inch tubing then straight to the filter which is protected by the heat shield, and also I do plan on being forced induction its just a matter of time.

Also I am not trying to make a "fast car" you could strap a rocket ship to the car and it would still be slow its 4000 pounds its about getting free power and improving on things.

I am looking for a body for my project a 95 and below sc300 with a lq4 with twin turbo backed by a holly dominator ecu and a lot of other stuff, that will be a fast car trying for 1000-1400 horse. I might end up just buying a built motor from texas speed, we will see when the time comes.

Also I have blown the doors off a v6 camaro so myth debunked haha

Thats the thing I have changed the power band of the car with the headers and when I install my exhaust it will really change the power band of the car since the headers I have no low end tq like I have said before I don't get into the power power untill 2800-3000 rpm thats were it starts.

Stock ecu's have the ability to compenscompensate about 10% for octane rating clogged air filter etc, I also plan on going the forced induction route later on.

Sure you outran a full .5 second faster car that's lighter with more power........

Its not free power as you seem to think it is since you are spending all this time and effort on a car that's not even tuned at the ECU that probably is just adjusting its way back to near stock like nearly everything does. Pull up your fuel trims and watch them, I'm willing to bet it's not going slightly lean like it should with additions like that since the ECU will just not open the throttle as much. Run your car in the 1/4 and see if it's any faster than stock since it won't be.

If you actually want to go faster you need to change something and have the ECU reprogrammed to ignore factory targets and mixture ratios. Otherwise you are wasting your time

haha you touch on something. My own brother baffles me sometimes, he said he and a coworker were messing around with his truck and tools from the factory (they do DoD work so you can bet it's tools we may never touch). He says they put his lug nuts back to one hundred forty seven inch pounds. It's a Ford Raptor. He's my brother so I corrected him. So I am saying many think like my brother, they don't really care to understand (I'm not saying that about anyone here it's a general statement that some folks are like my brother).

Anyway my daddy always told me there's no free lunch. Yesterday, a woman says John my schedule is free so just let me know when you want to have lunch in the next few weeks (our acct. mgr). So ok that's an exception.

As a general statement, imho many think that turbocharging is free. All the positives of a smaller displacement, all the benefits of a larger displacement. If it were like that, we'd call it the insurance business!

And I am not immune. I fell for the 2-5 HP by dropping in a K&N panel filter, back in 1998. I had to touch to stove and get burned.

You cant retune toyota/lexus ecu's so then how is it possible that the ppe headers give a 20hp and 20tq gain?

By the stock ECU maxing out its fuel trim allowance and then before it throws a lean code it decides to not allow full throttle opening, it WILL NOT exceed its 30% over stock fuel trim and will instead lean it out as much as it can before just closing the blade to get the fuel back to where it wants to see it.

All you are doing is using the very limited extra headroom in the ECU that anyone who just tunes it with NO hardware changes will exceed by 10hp if not a little more. Look at the US counterparts to the 3UZ-FE engine, they ALL pick up more than 25rwhp from zero hardware changes and just adjustment of spark timing and max fuel allowed and the desired targets. A same class tuned engine with headers like you have easily picks up 70-90 RWHP with a tune, you should be seeing nearly 50 on the 3UZ-FE but you are not because the ECU has not been told it's "new goal" and instead keeps trying to get your trims "back to center" as best it can.

yes you can quantum auto does it

It was not an option the time of that post the quantum auto ecu tuning is a very new, anything else?