It's the
snorkels in front of the core support under the bumper. Go look at the work
Velossatech did for the big mouth intakes. Seriously, the
snorkels under the bumper are great at hiding turbo noise but are an awful way to get air into the engine. It has to be gasping at high RPMs.
The stock design has very little space to pull air, so it has to be a major choke point over 3k rpm. There's less than an inch between the intake opening and a flat plastic panel. Seriously, drop the bumper - it only takes 10 minutes - it's really surprising. I installed the big mouth kit and it would easily suck your hand into the intake just revving in park, let alone under load!
All of the
aftermarket intake kits avoid that problem. Some, like
Velossatech and JT, replace the
snorkels with something much more rational. All the others don't, but the filters are exposed to a much larger air area, so they'll pull air from anywhere they can get it. Some have "shields", and while that will reduce the amount of direct hot air, it's nothing like a sealed system. Regardless, an open filter will get the air it wants.
My middle of the road is the big mouth
snorkels with K&N panels. Lowest cost and addresses the largest limitations.
re: heat soak, cooler air is almost always better. Starting cooler means it'll be cooler on the other side of the intercooler. While the intercooler makes the situation *less* bad, pulling in hot air still doesn't help. It's good to remember that air floating around the engine bay has mostly gone through the radiator, so it'll be anywhere from 140deg to 200deg - 100+ deg above ambient - before going through the turbo!
As a comparison point, I have the JT intercooler, K&N panels and big mouth
snorkels. Otherwise stock up front. I see IATs climb about 10deg while sitting at a light. That's heat soak in the intercooler and the JT intake piping. The system is sealed to pull air from in front of the car, so it's not drinking its own bathwater. When moving the IAT tends to be 10 to 20deg above ambient, then gains another 10deg while sitting. It works back down within a couple of minutes of moving again.
All that to say - underhood heat is certainly a factor in IAT, even if the engine isn't directly breathing underhood air!